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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Kleinian \(\sigma\)-function; Norton numbers; Weierstrass semigroup Komeda, J.; Matsutani, S.; Previato, E., The sigma function for Weierstrass semigroups \(\langle 3,7,8\rangle \) and \(\langle 6,13,14,15,16\rangle \), Int. J. Math., 24, 1350085, 58, (2013) Riemann surfaces; Weierstrass points; gap sequences, Plane and space curves, Analytic theory of abelian varieties; abelian integrals and differentials The sigma function for Weierstrass semigroups \(\langle 3,7,8\rangle\) and \(\langle 6,13,14,15,16\rangle\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic hyperelliptic function fields; imaginary quadratic function field; real quadratic function field; divisor class group; reduced ideals; group law [14]S. Paulus and H.-G. Rück, Real and imaginary quadratic representations of hyperelliptic function fields, Math. Comput. 68 (1999), 1233--1241. Arithmetic theory of algebraic function fields, Class groups and Picard groups of orders, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry Real and imaginary quadratic representations of hyperelliptic function fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic divisor on a curve; Hurwitz formula; Puiseux expansion; Coates' algorithm; integral basis; Ford/Zassenhaus algorithm Arithmetic ground fields for curves, Software, source code, etc. for problems pertaining to algebraic geometry, Software, source code, etc. for problems pertaining to field theory, Divisors, linear systems, invertible sheaves, Arithmetic theory of algebraic function fields Au sujet de l'algorithme ''de Coates''. (Concerning the Coates algorithm)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic compactification; moduli space of stable Higgs bundles; Riemann surface; nilpotent cone Hausel, Tamás, Compactification of moduli of {H}iggs bundles, Journal für die Reine und Angewandte Mathematik. [Crelle's Journal], 503, 169-192, (1998) Families, moduli of curves (algebraic), Compactification of analytic spaces, Algebraic moduli problems, moduli of vector bundles, Riemann surfaces; Weierstrass points; gap sequences, Vector bundles on curves and their moduli Compactification of moduli of Higgs bundles
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Singh B. On the group of automorphisms of a function field of genus at least two. J Pure Appl Algebra, 4: 205--229 (1975) Arithmetic theory of algebraic function fields, Ramification and extension theory, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry On the group of automorphisms of a function field of genus at least two
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; proper holomorphic embeddings Forstnerič, F.; Wold, E.F., Embeddings of infinitely connected planar domains into \(\mathbb{C}^2\), Anal. PDE, 6, 2, 499-514, (2013) Embedding of analytic spaces, Stein spaces, Automorphism groups of \(\mathbb{C}^n\) and affine manifolds, Riemann surfaces; Weierstrass points; gap sequences Embeddings of infinitely connected planar domains into \(\mathbb C^2\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Goppa codes; Weierstrass pair; pure gap; minimum distance; Hermitian curve; two-point codes Matthews G.L.: The Weierstrass semigroup of an \(m\)-tuple of collinear points on a Hermitian curve. In: Mullen G.L., Poli A., Stichtenoth H. (eds.) Finite Fields and Applications: 7th International Conference, Fq7, Toulouse, France, 5-9 May 2003, pp. 12-24. Springer, Berlin Heidelberg (2004). 10.1007/978-3-540-24633-6_2. Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences, Bounds on codes Goppa codes with Weierstrass pairs
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic plane non-singular curves; automorphism groups Badr, Eslam and Bars, Francesc and Lorenzo García, Elisa, On twists of smooth plane curves, Mathematics of Computation, (None) Riemann surfaces; Weierstrass points; gap sequences, Automorphisms of curves, Plane and space curves, Special algebraic curves and curves of low genus On the locus of smooth plane curves with a fixed automorphism group
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic double coverings; unirational quasi-elliptic surfaces; classification of surfaces [Miy] Miyanishi, M.: Unirational quasi-elliptic surfaces. Japan J. Math.3, 395--416 (1977) Families, moduli, classification: algebraic theory, Arithmetic theory of algebraic function fields, Special surfaces, Rational and unirational varieties Unirational quasi-elliptic surfaces
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic function field; automorphism group Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Representations of groups as automorphism groups of algebraic systems On Galois groups of global fields of positive characteristic
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic random graph; topological graph theory; Belyi surfaces Gamburd, A. and Makover, E. (2002). On the genus of a random Riemann surface. Contemp. Math. 311 133--140. Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Random graphs (graph-theoretic aspects), Combinatorial probability On the genus of a random Riemann surface.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; first eigenvalue; Laplacian; Belyi surfaces R. Brooks and E. Makover, ''Belyi Surfaces,'' in Entire Functions in Modern Analysis (Bar-Ilan Univ., Ramat-Gan, 2001), Isr. Math. Conf. Proc. 15, pp. 37--46. Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences Belyi surfaces.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic number theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. Research exposition (monographs, survey articles) pertaining to number theory, Class field theory, Class field theory; \(p\)-adic formal groups, Ramification and extension theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Collected or selected works; reprintings or translations of classics Algebraic numbers and algebraic functions
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Galois representations Riemann surfaces; Weierstrass points; gap sequences, Commutative rings of differential operators and their modules Galois representations on holomorphic differentials: An addendum
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic abelian functions; \(P\)-functions; Kleinian sigma-functions; Weierstrass functions; trigonal curves; addition formula England M., Deriving bases for Abelian functions, Comput. Methods Funct. Theory, 2011, 11(2), 617--654 Jacobians, Prym varieties, Riemann surfaces; Weierstrass points; gap sequences, Theta functions and abelian varieties, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Relationships between algebraic curves and integrable systems Deriving bases for abelian functions
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic-geometry codes; towers of function fields; \(Q\)th-power map Leonard, D. A.: Finding the missing functions for one-point AG codes. IEEE trans. Inform. theory 47, No. 6, 2566-2573 (2001) Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic theory of algebraic function fields Finding the defining functions for one-point algebraic-geometry codes
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic compact Riemann surfaces; algebraic curves Kichoon Yang, Compact Riemann surfaces and algebraic curves, Series in Pure Mathematics, vol. 10, World Scientific Publishing Co., Singapore, 1988. Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry Compact Riemann surfaces and algebraic curves
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic bilinear complexity; congruence function fields; descent of function fields; tensor rank; finite fields; Artin--Schreier extensions Ballet, Stéphane; Le Brigand, Dominique; Rolland, Robert, On an application of the definition field descent of a tower of function fields.Arithmetics, geometry, and coding theory (AGCT 2005), Sémin. Congr. 21, 187-203, (2010), Soc. Math. France, Paris Number-theoretic algorithms; complexity, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves On an application of the definition field descent of a tower of function fields
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroups at \(m\) points; minimal generating set; discrepancy Castellanos, A.S., Tizziotti, G.: On Weierstrass semigroup at \(m\) points on curves of the form \(f(y) = g(x)\). J. Pure Appl. Algebra (2017). https://doi.org/10.1016/j.jpaa.2017.08.007 Riemann surfaces; Weierstrass points; gap sequences, Curves over finite and local fields On Weierstrass semigroup at \(m\) points on curves of the form \(f(y)=g(x)\)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function fields; class number one; Weil polynomials Arithmetic theory of algebraic function fields, Curves over finite and local fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry The relative class number one problem for function fields. I
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphisms; curves DOI: 10.4310/MRL.2000.v7.n1.a6 Automorphisms of curves, Arithmetic algebraic geometry (Diophantine geometry), Riemann surfaces; Weierstrass points; gap sequences Varieties without extra automorphisms. I: Curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroup of a point; \(K3\) surface; weighted projective plane; numerical semigroup; double cover of a curve \(K3\) surfaces and Enriques surfaces, Coverings of curves, fundamental group, Plane and space curves, Riemann surfaces; Weierstrass points; gap sequences, Commutative semigroups Curves on weighted \(K3\) surfaces of degree two with symmetric Weierstrass semigroups
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Osculating surface; diophantine equation Diophantine equations, Enumerative problems (combinatorial problems) in algebraic geometry Note on the degree of osculating surfaces.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Arf numerical semigroup; numerical semigroup; sparse numerical semigroup; Weierstrass semigroup; weight of numerical semigroup Commutative semigroups, Riemann surfaces; Weierstrass points; gap sequences On certain families of sparse numerical semigroups with Frobenius number even
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroup; discrete manis valuation; Poincaré series Riemann surfaces; Weierstrass points; gap sequences, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series On Weierstrass semigroups at one and two points and their corresponding Poincaré series
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite field; optimal curve; Ree curve; Weierstrass semigroup Arithmetic ground fields for curves, Riemann surfaces; Weierstrass points; gap sequences, Geometric methods (including applications of algebraic geometry) applied to coding theory On the Ree curve
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic real abelian varieties; real structures on complex varieties; real curves; compact Riemann surface Ciro Ciliberto and Claudio Pedrini, Real abelian varieties and real algebraic curves, Lectures in real geometry (Madrid, 1994) De Gruyter Exp. Math., vol. 23, de Gruyter, Berlin, 1996, pp. 167 -- 256. Analytic theory of abelian varieties; abelian integrals and differentials, Riemann surfaces; Weierstrass points; gap sequences, Real-analytic and semi-analytic sets, Real-analytic manifolds, real-analytic spaces, Compact Riemann surfaces and uniformization Real abelian varieties and real algebraic curves
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass points; algebraic curve; gaps Komeda, J.: On the existence of Weierstrass points whose first non gaps are five. Manuscripta Math. \textbf{76} (1992) Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences On the existence of Weierstrass points whose first non-gaps are five
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic complex polynomials; algebraic equations; Riemann surfaces; monodromy group; Galois theory; solvability by radicals; Chebyshev polynomials; multivalued analytic functions Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Polynomials in real and complex fields: location of zeros (algebraic theorems), Equations in general fields, Compact Riemann surfaces and uniformization, Separable extensions, Galois theory, Riemann surfaces; Weierstrass points; gap sequences Variations on the theme of solvability by radicals
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic curves; Weierstrass points; bielliptic involution; Wiman' curve Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Automorphisms of curves A curve of genus 5 having 24 Weierstrass points of weight 5
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic closed non-orientable surfaces; periodic self homomorphisms; mapping class group; Klein surfaces Gromadzki, G.; Szepietowski, B.: On topological type of periodic self-homeomorphisms of closed non-orientable surfaces. Rev. R. Acad. cienc. Exactas fís. Nat., ser. A mat., RACSAM (2015) Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences, Group actions on manifolds and cell complexes in low dimensions On topological type of periodic self-homeomorphisms of closed non-orientable surfaces
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic norm form equation; torsion points in Jacobians; generalized Pell equation; Dirichlet unit theorem; continued fraction expansion; Pell- Fermat equation Multiplicative and norm form equations, Special algebraic curves and curves of low genus, Continued fractions, Arithmetic theory of algebraic function fields Equation de Pell et points d'ordre fini. (Pell equation and points of finite order)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic smooth projective curve; inflection points; Weierstrass point Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Plane and space curves The inflection points of high multiplicity on smooth plane curves and Weierstrass points
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic transcendental field extensions; Galois group; elliptic function fields Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Transcendental field extensions, Galois theory Un exemple de groupe de Galois d'une extension transcendante
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Families, moduli of curves (analytic), Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Cutting and pasting of Riemann surfaces with abelian differentials. I.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic characteristic \(p\); Weierstrass points on a smooth curve; order-sequence; base-point-free linear system Esteves, E.; Homma, M., Order sequences and rational curves, 27-42, (1994), Dekker, New York Riemann surfaces; Weierstrass points; gap sequences, Divisors, linear systems, invertible sheaves Order sequences and rational curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic curves; finite ground field; minimal algebraic complexities; multiplication; algebras over finite fields; coding theory; algebraic geometrical methods; Goppa codes D. V. Chudnovsky and G. V. Chudnovsky, ''Algebraic complexities and algebraic curves over finite fields,'' J. Complexity, 4, 285--316 (1988). Analysis of algorithms and problem complexity, Arithmetic codes, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Arithmetic ground fields for curves, Algebraic functions and function fields in algebraic geometry, Riemann-Roch theorems Algebraic complexities and algebraic curves over finite fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic wave equation; Dirichlet problem; Poncelet problem; Pell-Abel equation; uniqueness; dynamical systems on ellipses V. P. Burskiĭ and A. S. Zhedanov, The Dirichlet problem for the equation of string vibration, the Poncelet problem, the Pell-Abel equation, and some other related problems, Ukraïn. Mat. Zh. 58 (2006), no. 4, 435 -- 450 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 58 (2006), no. 4, 487 -- 504. Initial-boundary value problems for second-order hyperbolic equations, Wave equation, Diophantine equations, Projective techniques in algebraic geometry, Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic principal holomorphic bundle; Riemann surface Differentials on Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) On holomorphic principal bundles on a Riemann surface.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Belyi's theorem; abc; moduli of curves W. Goldring, ''Unifying themes suggested by Belyi's theorem,'' in: \textit{Number Theory, Analysis and Geometry}, Springer-Verlag (2011), pp. 181-214. Arithmetic aspects of dessins d'enfants, Belyĭ theory, Diophantine equations, Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Coverings of curves, fundamental group Unifying themes suggested by Belyi's theorem
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic degeneration of linear system; ramification points; limits of Weierstrass points; families of curves; limit linear systems Esteves, E, Linear systems and ramification points on reducible nodal curves, Mathematica Contemporanea, 14, 21-35, (1998) Divisors, linear systems, invertible sheaves, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic) Linear systems and ramification points on reducible nodal curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic arithmetic theory of algebraic function fields; towers of function fields; Zink's bound; Hasse-Witt invariant; \(p\)-rank [2]A. Bassa and P. Beelen, The Hasse--Witt invariant in some towers of function fields over finite fields, Bull. Brazil. Math. Soc. 41 (2010), 567--582. Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry The Hasse-Witt invariant in some towers of function fields over finite fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic automorphisms of surfaces; NEC groups; universal covering transformation groups; ovals; fixed-point sets; cyclic automorphism groups; Klein surfaces; numbers of fixed points Izquierdo, M.; Singerman, D.: On the fixed-point set of automorphisms of non-orientable surfaces without boundary. Geom. \& topol. Monogr. 1, No. The Epstein Birthday Schrift, 295-301 (1998) Automorphisms of infinite groups, Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Hyperbolic and elliptic geometries (general) and generalizations, Riemann surfaces; Weierstrass points; gap sequences, Other geometric groups, including crystallographic groups On the fixed-point set of automorphisms of non-orientable surfaces without boundary
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Representations of associative Artinian rings Weighted projective lines and Riemann surfaces
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic esquisse d'un programme; dessins des enfants; Grothendieck dessins; hypermaps on Riemann surfaces; Belyi functions Wolfart, Jürgen, The ``obvious'' part of Belyi's theorem and Riemann surfaces with many automorphisms. Geometric Galois actions, 1, London Math. Soc. Lecture Note Ser. 242, 97-112, (1997), Cambridge Univ. Press, Cambridge Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Coverings of curves, fundamental group The `obvious' part of Belyi's theorem and Riemann surfaces with many automorphisms
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroups; GK curve; AG codes Castellanos, A. S.; Tizziotti, G., Weierstrass semigroup and pure gaps at several points on the GK curve, Bull. Braz. Math. Soc., (2017) Riemann surfaces; Weierstrass points; gap sequences, Curves over finite and local fields Weierstrass semigroup and pure gaps at several points on the \(GK\) curve
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic functions in two variables; Riemann-Roch theorem; function fields Heinrich W. E. Jung, Einführung in die Theorie der algebraischen Funktionen zweier Veränderlicher, Akademie Verlag, Berlin, 1951 (German). Arithmetic theory of algebraic function fields, Research exposition (monographs, survey articles) pertaining to number theory, Algebraic functions and function fields in algebraic geometry Einführung in die Theorie der algebraischen Funktionen zweier Veränderlicher
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic-geometry codes; survey; class field towers; Galois rings; binary nonlinear codes; distribution of symbols Research exposition (monographs, survey articles) pertaining to information and communication theory, Geometric methods (including applications of algebraic geometry) applied to coding theory, Algebraic coding theory; cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Arithmetic theory of algebraic function fields Various constructions of good codes
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass \(n\)-semigroup; smooth curve; semigroup of non-gaps Ballico, E., On the Weierstrass semigroups of \(n\) points of a smooth curve, Archiv der Math., 104, 207-215, (2015) Riemann surfaces; Weierstrass points; gap sequences On the Weierstrass semigroups of \(n\) points of a smooth curve
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic nodal plane curves; Weierstrass gap sequence Coppens, M.; Kato, T.: The Weierstrass gap sequences at an inflection point on a nodal plane curve, aligned inflection points on plane curves, Boll. unione mat. Ital. sez. B (7) 11, 1-33 (1997) Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings The Weierstrass gap sequence at an inflection point on a nodal plane curve, aligned inflection points on plane curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surface; periods; symmetric product of a complex smooth projective algebraic curve; Jacobian; Abel's theorem Riemann surfaces; Weierstrass points; gap sequences, Analytic theory of abelian varieties; abelian integrals and differentials, Jacobians, Prym varieties, Differentials on Riemann surfaces, Singularities of curves, local rings Integration of algebraic functions and the Riemann-Kempf singularity theorem
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic hyperelliptic curves; elliptic and hyperelliptic cryptography; Jacobians; index calculus; Weil descent M.J. Jacobson, Jr., A.J. Menezes and A. Stein, Hyperelliptic curves and cryptography , %in High primes and misdemeanours : Lectures in honour of the Amer. Math. Soc., Fields Institute Communications Series { 41 (2004), 255-282% Providence (Rhode Island), 2004.. Cryptography, Arithmetic theory of algebraic function fields, Number-theoretic algorithms; complexity, Continued fraction calculations (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry Hyperelliptic curves and cryptography
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic K. Feng and W. Gao, Bernoulli-Goss polynomials and class numbers of cyclotomic function fields, preprint. Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Cyclotomic extensions, Special polynomials in general fields, Algebraic functions and function fields in algebraic geometry Bernoulli-Goss polynomial and class number of cyclotomic function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic Hecke character; function fields; weight B. H. Gross, Algebraic Hecke characters for function fields , Seminar on Number Theory, Paris 1980-81 (Paris, 1980/1981), Progr. Math., vol. 22, Birkhäuser Boston, Mass., 1982, pp. 87-90. Arithmetic theory of algebraic function fields, Adèle rings and groups, Finite ground fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Algebraic Hecke characters for function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic curve; adjunction theory; normalisation; Weierstraß semigroup Riemann surfaces; Weierstrass points; gap sequences, Semigroups On multi-index filtrations associated to Weierstraß semigroups
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic tower of function fields; genus; rational places; curves with many points A. Garcia, H. Stichtenoth, On the Galois closure of towers, preprint, 2005 Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Asymptotics for the genus and the number of rational places in towers of function fields over a finite field
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Galois groups of function fields; unramified cohomology; universal spaces; anabelian geometry Galois cohomology, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Cohomology of groups Universal spaces for unramified Galois cohomology
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic cubic function fields; ramification; families; explicit aspects Cubic and quartic extensions, Arithmetic theory of algebraic function fields, Quadratic extensions, Algebraic functions and function fields in algebraic geometry, Families, moduli of curves (algebraic) Cubic function fields with prescribed ramification
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann surfaces; Abelian integrals; algebraic number theory; function fields; valuations; function fields of curves; Abel-Jacobi theorem Cohn, P. M.: Algebraic numbers and algebraic functions, Chapman \& Hall math. Ser. (1991) Algebraic number theory: global fields, Arithmetic theory of algebraic function fields, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory, Algebraic functions and function fields in algebraic geometry Algebraic numbers and algebraic functions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic function field; Carlitz module; shtuka; unit group; class group L. Taelman, ''The Carlitz shtuka,'' J. Number Theory, vol. 131, iss. 3, pp. 410-418, 2011. Drinfel'd modules; higher-dimensional motives, etc., Zeta and \(L\)-functions in characteristic \(p\), Arithmetic theory of algebraic function fields, Motivic cohomology; motivic homotopy theory The Carlitz shtuka
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Galois point; Galois Weierstrass point; weak Galois Weierstrass point; pseudo-Galois Weierstrass point Riemann surfaces; Weierstrass points; gap sequences, Algebraic functions and function fields in algebraic geometry, Automorphisms of curves, Plane and space curves Relating Galois points to weak Galois Weierstrass points through double coverings of curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Special algebraic curves and curves of low genus, Elliptic curves, Riemann surfaces; Weierstrass points; gap sequences, Relationships between algebraic curves and physics, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic mirror symmetry, Proceedings of conferences of miscellaneous specific interest Higher genus curves in mathematical physics and arithmetic geometry. AMS special session, Seattle, WA, USA, January 8, 2016. Proceedings
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic arithmetical dynamical system; canonical height; division group; division point; Erdős-Turán Theorem; integral point; Koksma's inequality; linear forms in logarithms; logarithmic equidistribution; multiplicative group; Weyl sums Heights, Approximation in non-Archimedean valuations, Distribution modulo one, Linear forms in logarithms; Baker's method, Weyl sums, Global ground fields in algebraic geometry, Arithmetic varieties and schemes; Arakelov theory; heights, Linear algebraic groups over global fields and their integers, Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps, Arithmetic properties of periodic points Distribution of integral division points on the algebraic torus
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic finite zone solutions; Toda chains; Poincaré series; Schottky uniformisation; hyperelliptic Riemannian surface Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Theta functions and curves; Schottky problem Uniformisation of Riemann surfaces and Toda chain
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic nongap sequence of a Weierstrass point; coverings of elliptic curves E. Ballico, C. Keem, Weierstrass multiple points on algebraic curves and ramified coverings, Israel. J. Math. Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, Vector bundles on curves and their moduli Weierstrass multiple points on algebraic curves and ramified coverings
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Riemann's existence theorem; branched cover; fundamental group; field of definition History of mathematics in the 19th century, History of algebraic geometry, Coverings of curves, fundamental group, Riemann surfaces; Weierstrass points; gap sequences, History of functions of a complex variable, Compact Riemann surfaces and uniformization Riemann's existence theorem
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Grassmann manifold of two dimensional subspaces of space of polynomials; rational maps; Catalan number; enumerative geometry; Schubert calculus \beginbarticle \bauthor\binitsL. \bsnmGoldberg, \batitleCatalan numbers and branched coverings by the Riemann sphere, \bjtitleAdv. Math. \bvolume85 (\byear1991), no. \bissue2, page 129-\blpage144. \endbarticle \OrigBibText L. Goldberg, Catalan numbers and branched coverings by the Riemann sphere, Adv. Math. 85 (1991), no. 2, 129-144. \endOrigBibText \bptokstructpyb \endbibitem Coverings of curves, fundamental group, Grassmannians, Schubert varieties, flag manifolds, Polynomials and rational functions of one complex variable, Riemann surfaces; Weierstrass points; gap sequences, Enumerative problems (combinatorial problems) in algebraic geometry Catalan numbers and branched coverings by the Riemann sphere
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Brauer group; quadratic forms; \(u\)-invariant; complete discretely valued fields; function fields Parimala, R.; Suresh, V., On the \(u\)-invariant of function fields of curves over complete discretely valued fields, Adv. Math., 280, 729-742, (2015) Arithmetic theory of algebraic function fields, Algebraic theory of quadratic forms; Witt groups and rings, Brauer groups of schemes On the \(u\)-invariant of function fields of curves over complete discretely valued fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic topological quantum field theories; anomalies; three-dimensional topology; Riemann surfaces; geometric and deformation quantization; index theorem; exotic spheres Baadhio, R. A.: Quantum topology and global anomalies. Princeton series in physics (1995) Applications of global analysis to the sciences, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Anomalies in quantum field theory, Research exposition (monographs, survey articles) pertaining to global analysis, Research exposition (monographs, survey articles) pertaining to quantum theory, Teichmüller theory for Riemann surfaces, Applications of differential geometry to physics, General geometric structures on low-dimensional manifolds, Riemann surfaces; Weierstrass points; gap sequences Quantum topology and global anomalies
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Klein's surface; theta function; theta constant; proportionalities of theta constant; period matrix Theta functions and curves; Schottky problem, Riemann surfaces; Weierstrass points; gap sequences Klein's surface of genus three and associated theta constants.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic codes; singular plane models; adjoints; symbolic Hamburger-Noether expressions; Weierstrass semigroup; Singular; plane curve singularities Campillo, A., Farrán, J.I.: Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes. Math. Comput. 71, 1759-1780 (2001) Computational aspects of algebraic curves, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects), Riemann surfaces; Weierstrass points; gap sequences, Geometric methods (including applications of algebraic geometry) applied to coding theory Symbolic Hamburger-Noether expressions of plane curves and applications to AG codes
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic absolutely irreducible polynomials; algebraic functions; Hilbert irreducibility theorem Hilbertian fields; Hilbert's irreducibility theorem, Polynomials in general fields (irreducibility, etc.), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Independence of values of algebraic functions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroups of points; double coverings of curves; plane curves of degree 4 Komeda, J, On Weierstrass semigroups of double coverings of genus three curves, Semigroup Forum, 83, 479-488, (2011) Riemann surfaces; Weierstrass points; gap sequences On Weierstrass semigroups of double coverings of genus three curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroup; many-point algebraic geometric code; Kummer extension Riemann surfaces; Weierstrass points; gap sequences, Linear codes (general theory), Geometric methods (including applications of algebraic geometry) applied to coding theory Pure gaps on curves with many rational places
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic division algebra over function field; sheaf of differentials; maximal order; Riemann-Roch theorem; genus M. van den Bergh and J. Van Geel, Algebraic elements in division algebras over function fields of curves, Israel J. Math., 52 (1985), no. 1-2, 33--45. Zbl 0596.12012 MR 0815599 Quaternion and other division algebras: arithmetic, zeta functions, Transcendental field extensions, Skew fields, division rings, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Arithmetic theory of algebraic function fields, Division rings and semisimple Artin rings, Algebraic functions and function fields in algebraic geometry Algebraic elements in division algebras over function fields of curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic noncommutative regular projective curve; noncommutative function field; Auslander-Reiten translation; Picard-shift; ghost group; maximal order over a scheme; ramification; Witt curve; noncommutative elliptic curve; Klein bottle; Fourier-Mukai partner; weighted curve; orbifold Euler characteristic; noncommutative orbifold; tubular curve; finite dimensional algebra; Beilinson theorem Kussin, Dirk, Weighted noncommutative regular projective curves, J. Noncommut. Geom., 10, 4, 1465-1540, (2016) Noncommutative algebraic geometry, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Abelian categories, Grothendieck categories, Elliptic curves, Orders in separable algebras, Klein surfaces Weighted noncommutative regular projective curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass points for pluricanonical linear systems on an algebraic curve; higher order Weierstrass points; hyperelliptic curves; height Silverman, Some arithmetic properties of Weierstrass points: hyperelliptic curves, Bol. Soc. Bras. Mat. (N.S.) 21 (1) pp 11-- (1990) Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves Some arithmetic properties of Weierstrass points: Hyperelliptic curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Hall conjecture; non-constant polynomials; degree; lower bound; weighted trees; \(abc\) conjecture; Riemann existence theorem Zannier, U., On davenport's bound for the degree of \(f^3 - g^2\) and riemann's existence theorem, Acta Arith., 71, 2, 107-137, (1995) Diophantine inequalities, Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry On Davenport's bound for the degree of \(f^ 3 - g^ 2\) and Riemann's existence theorem
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic diophantine equation; elliptic curve; Fermat's \(m\)-tuple equations; \(S\)-integral points E. Herrmann, A. Pethö and H.G. Zimmer, On Fermat's quadruple equations, Abh. Math. Sem. Univ. Hamburg 69 (1999), no. 1, 283-291. Computer solution of Diophantine equations, Elliptic curves over global fields, Elliptic curves, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Diophantine equations On Fermat's quadruple equations
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic moduli space; Deligne-Mumford compactification; Weierstrass measure Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Integral representations; canonical kernels (Szegő, Bergman, etc.) Limit of Weierstrass measure on stable curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Wagner, M.: Über korrespondenzen zwischen algebraischen funktionenkörpern, (2009) Computational aspects of algebraic curves, Arithmetic ground fields for curves, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields On correspondences between algebraic function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Hodge structure; twisted cohomology group; Riemann surfaces M. Hanamura and M. Yoshida, \textit{Hodge structure on twisted cohomologies and twisted Riemann inequalities. I}, \textit{Nagoya Math. J.}\textbf{154} (1999) 123. Riemann surfaces; Weierstrass points; gap sequences, Variation of Hodge structures (algebro-geometric aspects), Étale and other Grothendieck topologies and (co)homologies Hodge structure on twisted cohomologies and twisted Riemann inequalities. I
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic generalized Weierstraß semigroup; complete intersection curve Delgado, F.: The symmetry of the Weierstrass generalized semigroups and affine embeddings. Proc. Am. Math. Soc. 108(3), 627--631 (1990) Riemann surfaces; Weierstrass points; gap sequences, Complete intersections The symmetry of the Weierstrass generalized semigroups and affine embeddings
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic valued fields; rigid analytic spaces; algebraic curves; constant reduction Valued fields, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Recent results in the theory of constant reductions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic global function fields; curves with many rational points; low-discrepancy sequences; Gilbert-Varshamov bound Niederreiter, H., Xing, Ch.: Global function fields with many rational places and their applications. In: Mullin, R.C., Mullen, G.L. (eds.) Finite Fields: Theory, Applications, and Algorithms, Waterloo, ON, 1997. Contemp. Math., vol. 225, pp. 87--111. Amer. Math. Soc., Providence (1999) Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Global function fields with many rational places and their applications
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic number of zeroes; real curve; JFM 34.0414.01 Riemann surfaces; Weierstrass points; gap sequences, Enumerative problems (combinatorial problems) in algebraic geometry, Real algebraic and real-analytic geometry Trigonometric tensors on algebraic curves of arbitrary genus. An analogue of the Sturm-Hurwitz theorem
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic numerical semigroup; Weierstrass semigroup; double cover of a curve; curve of genus two Harui, T., Komeda, J., Ohbuchi, A.: The Weierstrass semigroups on double covers of genus two curves, preprint Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Commutative semigroups The Weierstrass semigroups on double covers of genus two curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic towers of algebraic function fields; genus; number of places Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Quadratic recursive towers of function fields over \(\mathbb{F}_2\)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass points for line bundle on smooth curve; gap sequences Riemann surfaces; Weierstrass points; gap sequences, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Vector bundles on curves and their moduli Remark on the Weierstrass points on curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Turbek, P.: A necessary and sufficient condition for lifting the hyperelliptic involution. Proc. Am. Math. Soc. 125(3), 2615--2625 (1997) Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences A necessary and sufficient condition for lifting the hyperelliptic involution
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic geometric codes; one-point codes; explicit construction of integral basis; Drinfeld-Vladut bound Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Geometric methods (including applications of algebraic geometry) applied to coding theory, Applications to coding theory and cryptography of arithmetic geometry Towards a basis for the space of regular functions in a tower of function fields meeting the Drinfeld-Vladut bound
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic abelian varieties over finite fields; \(\ell\)-adic Tate modules; Riemann Hypothesis; Drinfeld module; isogeny; global zeta-functions Ernst-Ulrich Gekeler, On finite Drinfel\(^{\prime}\)d modules, J. Algebra 141 (1991), no. 1, 187 -- 203. Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Arithmetic ground fields for abelian varieties, Complex multiplication and abelian varieties, Curves over finite and local fields, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Finite ground fields in algebraic geometry On finite Drinfeld modules
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic String and superstring theories; other extended objects (e.g., branes) in quantum field theory, \(3\)-folds, Riemann surfaces; Weierstrass points; gap sequences, Relationships between algebraic curves and physics, Yang-Mills and other gauge theories in quantum field theory String duality and a new description of the \(E_6\) singularity
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic trees; Riemann surface; morphism; hyperelliptic curves F. Pakovich, ''On trees admitting morphisms onto hedgehogs or onto chains,'' Usp. Mat. Nauk, 55, No. 3, 593--594 (2000). Riemann surfaces; Weierstrass points; gap sequences, Trees, Coverings of curves, fundamental group, Arithmetic ground fields for curves On trees admitting morphisms onto hedgehogs or onto chains
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic canonical Green's function; hyperelliptic curves; Kawazumi-Zhang invariant; Weierstrass points Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Families, moduli of curves (analytic) Special values of canonical Green's functions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Hauptmodul; monstrous moonshine; Hilbert Class field Class field theory, Arithmetic theory of algebraic function fields, Complex multiplication and moduli of abelian varieties, Complex multiplication and abelian varieties, Special algebraic curves and curves of low genus On the evaluation of singular invariants for canonical generators of certain genus one arithmetic groups
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic affine curves; near weight functions; Gröbner basis; Weierstrass semigroups at several points Riemann surfaces; Weierstrass points; gap sequences, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Arithmetic theory of semigroups, Applications to coding theory and cryptography of arithmetic geometry On semigroups, Gröbner basis and algebras admitting a complete set of near weights
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic field extensions; specializations; local behavior; Hilbertian fields Arithmetic theory of algebraic function fields, Hilbertian fields; Hilbert's irreducibility theorem, Field arithmetic, Ramification problems in algebraic geometry Hilbert specialization results with local conditions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroups; algebraic geometric codes; codes on many points; Kummer extensions Geometric methods (including applications of algebraic geometry) applied to coding theory, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry, Riemann surfaces; Weierstrass points; gap sequences Algebraic geometric codes on many points from Kummer extensions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic higher derivations; algebraic function field; Taylor expansion Morphisms of commutative rings, Modules of differentials, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Higher derivations of algebraic function fields
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