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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 Horiuchi, R. and Tanimoto, T. Fixed points of automorphisms of compact Riemann surfaces and higher-order Weierstrass points. Proc. Amer. Math. Soc. 105, (1989), 856--860 Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences Fixed points of automorphisms of compact Riemann surfaces and higher- order 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 theta functions; Korteweg/de Vries equations; Riemann surfaces of infinite genus W. Müller, M. Schmidt, and R. Schrader, Theta functions for infinite period matrices , Internat. Math. Res. Notices (1996), no. 12, 565-587. Theta functions and abelian varieties, KdV equations (Korteweg-de Vries equations), Riemann surfaces; Weierstrass points; gap sequences, Period matrices, variation of Hodge structure; degenerations Theta functions for infinite period matrices
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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 Fuchsian groups; moduli spaces of parabolic bundles Bauer, S., Parabolic bundles, elliptic surfaces and \(\operatorname{SU}(2)\)-representation spaces of genus zero Fuchsian groups, Math. ann., 290, 3, 509-526, (1991), MR 1116235 Vector bundles on curves and their moduli, Fuchsian groups and their generalizations (group-theoretic aspects), Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Riemann surfaces; Weierstrass points; gap sequences Parabolic bundles, elliptic surfaces and \(SU(2)\)-representation spaces of genus zero Fuchsian 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 Carlitz module; Artin's conjecture; function fields Cyclotomic function fields (class groups, Bernoulli objects, etc.), Well-distributed sequences and other variations, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On extending Artin's conjecture to composite moduli in 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 Weierstrass points; higher-order Weierstrass points; superelliptic curves; branch points; numerical semigroups Shor, Caleb M., Higher-order Weierstrass weights of branch points on superelliptic curves, (Malmendier, A.; Shaska, T., Algebraic curves and their fibrations in mathematical physics and arithmetic geometry, Contemp. math., (2017), Amer. Math. Soc.), to appear Riemann surfaces; Weierstrass points; gap sequences, Curves of arbitrary genus or genus \(\ne 1\) over global fields Higher-order Weierstrass weights of branch points on superelliptic 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 semigroups of several points; linear systems; hyperelliptic curves Carvalho C.: On \({\mathcal V}\)-Weiertsrass sets and gaps. J. Algebra \textbf{312}, 956-962 (2007). Riemann surfaces; Weierstrass points; gap sequences On \(\mathcal V\)-Weierstrass sets and gaps
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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 10.3836/tjm/1219844828 Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Rationality questions in algebraic geometry On the moduli space of pointed algebraic curves of low genus. II. Rationality
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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 function fields; Poincaré residue; differential form; rank n discrete valuation Kawahara, Y., Uchibori, T.: On residues of differential forms in algebraic function fields of several variables. TRU Math.21, 173--180 (1985) Arithmetic theory of algebraic function fields, Morphisms of commutative rings, Transcendental field extensions, Valued fields, Algebraic functions and function fields in algebraic geometry, Relevant commutative algebra On residues of differential forms in algebraic function fields of several variables
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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 quantum completely integrable systems; Jacobi variety; Jacobi inversion problem J. C. Eilbeck, V. Z. Enolskii, and D. V. Leykin, ''On the Kleinian Construction of Abelian Functions of Canonical Algebraic Curves,'' in SIDE III: Symmetries and Integrability of Difference Equations: Proc. Conf., Sabaudia, Italy, 1998 (Am. Math. Soc., Providence, RI, 2000), CRM Proc. Lect. Notes 25, pp. 121--138. Jacobians, Prym varieties, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Riemann surfaces; Weierstrass points; gap sequences, KdV equations (Korteweg-de Vries equations) On the Kleinian construction of Abelian functions of canonical 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 endomorphism ring; stable reduction; good reduction; Tate parametrization; supersingular Drinfeld modules; Hasse invariant Gekeler E.-U.: Zur Arithmetik von Drinfeld-Moduln. Math. Ann. 262, 167--182 (1983) Drinfel'd modules; higher-dimensional motives, etc., Arithmetic ground fields for abelian varieties, Global ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Algebraic functions and function fields in algebraic geometry, Complex multiplication and abelian varieties, Complex multiplication and moduli of abelian varieties, Arithmetic theory of algebraic function fields Zur Arithmetik von Drinfeld-Moduln
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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 group; function field; Riemann surface; symmetric permutation; group; punctured spheres; moduli spaces Riemann surfaces; Weierstrass points; gap sequences, Separable extensions, Galois theory, Compact Riemann surfaces and uniformization, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group Galois theory and the uniformization of Riemann 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 automorphic form; Drinfeld's shtuka; global function field; Langlands conjecture; moduli stack of shtukas Laumon, G., La correspondance de Langlands sur LES corps de fonctions (d'après Laurent lafforgue), No. 276, 207-265, (2002) Langlands-Weil conjectures, nonabelian class field theory, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Modular forms associated to Drinfel'd modules, Algebraic moduli problems, moduli of vector bundles, Representation-theoretic methods; automorphic representations over local and global fields The Langlands correspondence for function fields (after Laurent Lafforgue)
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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; constant reduction; valuation prolongation; geometric family; Skolem property; principal family; birational characterization of arithmetic surfaces B. Green, Geometric families of constant reductions and the Skolem property, Trans. Amer. Math. Soc. 350 (1998), no. 4, 1379-1393. Valued fields, Arithmetic theory of algebraic function fields, Arithmetic ground fields for surfaces or higher-dimensional varieties, Global ground fields in algebraic geometry Geometric families of constant reductions and the Skolem property
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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 genus of curves over finite fields; many rational points; maximal function fields R. Fuhrmann and F. Torres. The genus of curves over finite fields with many rational points. Manuscripta Math., 89(1) (1996), 103--106. Curves over finite and local fields, Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Special algebraic curves and curves of low genus, Arithmetic ground fields for curves The genus of curves over finite fields with many rational 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 Bonelli, G.; Maruyoshi, K.; Tanzini, A., Quantum Hitchin Systems via \({\beta}\)-Deformed Matrix Models, Commun. Math. Phys., 358, 1041, (2018) Quantization in field theory; cohomological methods, Yang-Mills and other gauge theories in quantum field theory, Supersymmetric field theories in quantum mechanics, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Topological field theories in quantum mechanics, Riemann surfaces; Weierstrass points; gap sequences Quantum Hitchin systems via \(\beta\)-deformed matrix models
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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; Pólya ring; integer valued polynomials F. J. Van Der Linden, Integer valued polynomials over function fields, \(Nederl. Akad. Wetensch. Indag. Math.\)50 (1988), 293-308. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Polynomials over finite fields Integer valued polynomials over 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 Hilbert's tenth Problem; Undecidability; Elliptic curves; Quadratic forms; Rational points; Diophantine model Eisenträger, K., Hilbert's tenth problem for function fields of varieties over number fields and p-adic fields, J. Algebra, 310, 775-792, (2007) Decidability (number-theoretic aspects), Basic properties of first-order languages and structures, Rational points, Arithmetic theory of algebraic function fields Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic 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 field extension; valuation ring; ultrapower Popescu, D.: On Zariski's uniformization theorem. Lect. notes in math. 1056 (1984) Applications of logic to commutative algebra, Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.), Arithmetic theory of algebraic function fields, Valuation rings, Field extensions, Principal ideal rings, Relevant commutative algebra On Zariski's uniformization 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 inverse problem of Galois theory; Fischer-Griess monster as Galois group over \({\mathbb{Q}}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_ 2({\mathbb{R}})\); congruence subgroup; modular curve; Puiseux-series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps; lectures Galois theory, Simple groups: sporadic groups, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Simple groups: alternating groups and groups of Lie type, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Some finite groups which appear as Gal L/K, where \(K\subseteq {\mathbb{Q}}(\mu _ n)\)
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 Klein surfaces; genus; Riemann surfaces; NEC groups; alternating groups; Hurwitz groups; \(H^*\)-groups Generators, relations, and presentations of groups, Fuchsian groups and their generalizations (group-theoretic aspects), Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Compact Riemann surfaces and uniformization, Automorphisms of curves, Riemann surfaces; Weierstrass points; gap sequences, Classification theory of Riemann surfaces, Discrete subgroups of Lie groups Alternating groups as automorphism groups of 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 Function theory on compact Riemann surfaces spread over the Riemann sphere Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization Remarks on the article ``On the theory of Riemann's integrals'' by H.F. Baker, V. 45 of Mathematische Annalen.
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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 elliptic modular functions; function field; higher level; Jacobi functions; Shimura reciprocity law Berndt, Rolf, Sur l'arithmétique du corps des fonctions elliptiques de niveau~{\(N\)}, Seminar on Number Theory, {P}aris 1982--83 ({P}aris, 1982/1983), Progr. Math., 51, 21-32, (1984), Birkhäuser Boston, Boston, MA Modular and automorphic functions, Jacobi forms, Arithmetic theory of algebraic function fields, Homogeneous spaces and generalizations, General theory of automorphic functions of several complex variables On the arithmetic of the elliptic function field of level \(N\)
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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 function fields; Galois theory of function fields; Kummer theory; valuations; flag functions F.\ A. Bogomolov and Y. Tschinkel, Commuting elements of Galois groups of function fields, Motives, polylogarithms and Hodge theory. Part I (Irvine 1998), Int. Press Lect. Ser. 3, International Press, Somerville (2002), 75-120. Arithmetic theory of algebraic function fields, Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Configurations and arrangements of linear subspaces Commuting elements in Galois groups of 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 Weierstrass points; bielliptic curves; ramification points J. Park,A note on Weierstrass points on bielliptic curves, Manuscripta Math.,95 (1998), pp. 33--45. Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves A note on Weierstrass points of bielliptic 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, Rational points Generalizations of Golod-Shafarevich and applications
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 inverse Galois problem; Galois extension of function field; Riemann- Hurwitz formula; genus; mock covers of curves DOI: 10.2307/2159335 Algebraic functions and function fields in algebraic geometry, Inverse Galois theory, Birational automorphisms, Cremona group and generalizations, Automorphisms of curves, Arithmetic theory of algebraic function fields, Curves in algebraic geometry The automorphism group of a function 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 Weierstrass gaps; minimum distance of Goppa codes; algebraic-geometric codes García, Arnaldo; Kim, Seon Jeong; Lax, Robert F., Consecutive Weierstrass gaps and minimum distance of Goppa codes, J. pure appl. algebra, 84, 2, 199-207, (1993), MR 1201052 Linear codes (general theory), Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences Consecutive Weierstrass gaps and minimum distance of Goppa 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 exponentiation; Parshin completion; maximal flag; Goss zeta function; higher dimensional varieties; ample divisor Kapranov, M.: A higher-dimensional generalization of the goss zeta function. J. number theory 50, 363-375 (1995) Arithmetic theory of algebraic function fields, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of polynomial rings over finite fields, Varieties over finite and local fields, Finite ground fields in algebraic geometry A higher-dimensional generalization of the Goss zeta function
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 bielliptic curve; bielliptic involution; Fermat quartic; double covering of the Fermat's quartic del Centina A.: On certain remarkable curves of genus five. Indag. Math., N.S. 15, 339--346 (2004) Special algebraic curves and curves of low genus, Plane and space curves, Riemann surfaces; Weierstrass points; gap sequences, Projective techniques in algebraic geometry On certain remarkable curves of genus five.
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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; Riemann-Roch theorem; meromorphic functions Riemann surfaces; Weierstrass points; gap sequences The Riemann-Roch theorem on 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 vanishing cycles; function fields Arithmetic theory of algebraic function fields, Zeta and \(L\)-functions in characteristic \(p\), Structure of families (Picard-Lefschetz, monodromy, etc.) Singularities and vanishing cycles in number theory over 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 Silverman, J. H., Generalized greatest common divisors, divisibility sequences, and vojta\(###\)s conjecture for blowups, Monatsh. Math., 145, 4, 333-350, (2005) Varieties over global fields, Diophantine inequalities, Diophantine inequalities, Global ground fields in algebraic geometry Generalized greatest common divisors, divisibility sequences, and Vojta's conjecture for blowups
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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 error-correcting codes; curves over finite fields 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, Algebraic coding theory; cryptography (number-theoretic aspects), Algebraic functions and function fields in algebraic geometry Upper and lower bounds for \(A(q)\)
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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 minimum distance of Goppa codes; Weierstrass gaps García, Arnaldo; Lax, R.F., Goppa codes and Weierstrass gaps, (), 33-42, MR 1186414 Geometric methods (including applications of algebraic geometry) applied to coding theory, Computational aspects of algebraic curves, Linear codes (general theory), Riemann surfaces; Weierstrass points; gap sequences Goppa codes and Weierstrass gaps
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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 geometric theory of algebraic functions of one variable; Riemann-Roch theorem; algebraically perfect fields W. L. Chow, Die geometrische Theorie der algebraischen Funktionen für beliebige vollkommene Körper, Math. Ann. (1937) pp. 656-682. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Die geometrische Theorie der algebraischen Funktionen für beliebige vollkommene Körper
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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 function field; automorphisms of rational function field; Lüroth extensions; \(PSL({\mathbb{F}}_ q)\); holomorphic differentials; different; genus Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The genera of \(PSL({\mathbb{F}}_ q)\)-Lüroth 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 Kummer cover; Artin-Schreier cover; maximal curves Arithmetic theory of algebraic function fields, Curves over finite and local fields, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry Fibre products of Kummer and Artin-Schreier 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 Wronski system; gap sequence; Weierstrass points Laksov, D. and Thorup, A.: Weierstraß points and gap sequences for families of curves, Preprint, 1993. Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic) Weierstrass points and gap sequences for families 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 modular curves; optimal towers; algebraic-geometric codes Li, W. -C.W.: Modularity of asymptotically optimal towers of function fields. Coding, cryptography and combinatorics, 51-65 (2004) Applications to coding theory and cryptography of arithmetic geometry, Rational points, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic theory of algebraic function fields Modularity of asymptotically optimal towers of 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 hyperelliptic function field; quasi-periodic continued fraction expansions; quasi-periodicity; periodicity Arithmetic theory of algebraic function fields, Continued fractions and generalizations, Algebraic functions and function fields in algebraic geometry Periodicity of continued fractions in hyperelliptic 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 finite field; towers of algebraic function fields Arithmetic theory of algebraic function fields, Class field theory, Algebraic functions and function fields in algebraic geometry, Rational points A note on 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 hyperelliptic surface; gonality of surfaces Bujalance, E., Etayo, J.J., Gamboa, J.M., Gromadzki, G.: The gonality of Riemann surfaces under projections by normal coverings, Preprint (2009) Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences The gonality of Riemann surfaces under projections by normal 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 finite fields; Riemann-Weil hypothesis; Weierstrass points Stöhr, K. O.; Voloch, J. F., Weierstrass points and curves over finite fields, Proc. Lond. Math. Soc., 52, 1-19, (1986) Finite ground fields in algebraic geometry, Curves over finite and local fields, Rational points, Riemann surfaces; Weierstrass points; gap sequences Weierstrass points and 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 Riemann surfaces; Klein surfaces; vector bundles; spin structure Klein surfaces, Riemann surfaces; Weierstrass points; gap sequences, Vector bundles on curves and their moduli Discrete subgroups of GL(2, C) and spinor bundles on Riemann and Klein 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 complex algebraic curves; compact Riemann surfaces; group actions; automorphism groups; integration theory; divisors; Riemann-Roch theorem; Abel's theorem; line bundles R. Miranda, \textit{Algebraic Curves and Riemann Surfaces}, Graduate Studies in Mathematics, Vol. 5, American Mathematical Society, 1995. Riemann surfaces; Weierstrass points; gap sequences, Riemann surfaces, Jacobians, Prym varieties, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, Divisors, linear systems, invertible sheaves Algebraic curves 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 compact Riemann surfaces; automorphisms; fixed points; Weierstrass weights Perez del Pozo, AL, On the weights of fixed points of automorphism of a compact Riemann surface, Arch. Math., 86, 50-55, (2006) Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization On the weights of the fixed points of an automorphism of a compact 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 graph coloring algorithm; tiling Coloring of graphs and hypergraphs, Diophantine equations, Graph algorithms (graph-theoretic aspects), Arithmetic problems in algebraic geometry; Diophantine geometry Algorithm for generating and map-coloring of a special type of rectangular Diophantine carpets
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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, Separable extensions, Galois theory, Algebraic functions and function fields in algebraic geometry, Zeta functions and \(L\)-functions of number fields Errata in ``On dihedral 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 Arakelov theory; arithmetic surfaces; compact Riemann surfaces; moduli spaces; Riemann-Roch theorems; hyperbolic geometry; modular forms Arithmetic varieties and schemes; Arakelov theory; heights, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (analytic), Curves of arbitrary genus or genus \(\ne 1\) over global fields \(\Omega\)-admissible theory.
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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 mass formula; abelian varieties over finite fields Varieties over finite and local fields, Arithmetic ground fields for abelian varieties, Arithmetic theory of algebraic function fields On counting certain abelian varieties 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 Galois extension; Galois group; \(G\)-covering; \(\mathbb{Q}_ p\)-rational points; inverse Galois problem Deschamps, B.: Existence de points p-adiques pour tout p sur un espace de Hurwitz. Proceedings AMS-NSF Summer Conference, 186, Cont. Math. series, Recent Developments in the Inverse Galois Problem, 111--171 (1995) Rational points, Inverse Galois theory, Coverings of curves, fundamental group, Arithmetic theory of algebraic function fields Existence of \(p\)-adic points for all \(p\) over a Hurwitz space
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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 curve; linear system; inflection point Special divisors on curves (gonality, Brill-Noether theory), Riemann surfaces; Weierstrass points; gap sequences Generalized inflection points of very general effective divisors on smooth 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 inverse problem of Galois theory; Fischer-Griess monster as Galois group over \(\mathbb{Q}\); finite simple groups; fundamental group; rigid simple groups; cyclotomic field; discrete subgroups of \(PSL_2(\mathbb{R})\); congruence subgroup; modular curve; Puiseux series; group of covering transformations; compact Riemann surface; algebraic function field; ramification points; cusps J. Thompson , Some finite groups which appear as Gal (L/K) where K \subset Q(\mu n) , J. Alg. 89 (1984) 437-499. Galois theory, Simple groups: sporadic groups, Representations of groups as automorphism groups of algebraic systems, Arithmetic theory of algebraic function fields, Simple groups: alternating groups and groups of Lie type, Unimodular groups, congruence subgroups (group-theoretic aspects), Finite automorphism groups of algebraic, geometric, or combinatorial structures, Compact Riemann surfaces and uniformization, Algebraic functions and function fields in algebraic geometry, Separable extensions, Galois theory Some finite groups which appear as \(\mathrm{Gal } L/K\), where \(K\subseteq \mathbb{Q}(\mu_n)\)
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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 real multiplication; Prym locus; Teichmüller curve Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\), Riemann surfaces; Weierstrass points; gap sequences, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Weierstrass Prym eigenforms in genus four
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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 function field; no movable singularity; strongly normal extension; weakly normal Differential algebra, Arithmetic ground fields for curves, Group actions on varieties or schemes (quotients), \(p\)-adic differential equations, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields Movable singularities and differential Galois theory
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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 Hilbert's 10th problem; algebraic integers; local-global principle; solvability of diophantine equations B. Green, F. Pop, P. Roquette, On Rumely's local-global principle. \textit{Jahresber. Deutsch. Math.-Verein}. \textbf{97} (1995), 43-74. MR1341772 Zbl 0857.11033 Varieties over global fields, Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry On Rumely's local-global principle
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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; compact Riemann surfaces Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Automorphisms of curves Low genera curves with 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 compactification; Drinfeld modules Formal groups, \(p\)-divisible groups, Arithmetic theory of algebraic function fields, Structure of families (Picard-Lefschetz, monodromy, etc.) Compactification of the scheme of 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 inverse Galois problem; \(\ell\)-adic representations; abelian analytic functions Modular correspondences, etc., Arithmetic aspects of modular and Shimura varieties, Arithmetic theory of algebraic function fields, Coverings of curves, fundamental group, General theory for finite permutation groups Moduli relations between \(\ell\)-adic representations and the regular inverse Galois problem
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 invariant field of automorphism group; rational function field; rationality problem Rational and unirational varieties, Group actions on varieties or schemes (quotients), Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Actions of groups on commutative rings; invariant theory Finite group actions on rational 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 cyclotomic function field; Jacobian; Hasse-Witt invariant Cyclotomic function fields (class groups, Bernoulli objects, etc.), Arithmetic theory of algebraic function fields, Jacobians, Prym varieties On the ordinarity of the maximal real subfield of cyclotomic 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 zeta functions; pseudo-periods M. Heins,On the pseudo-periods of the Weierstrass zeta function, Nagoya Math. J.30 (1967), 113--119. Modular and automorphic functions, Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Elliptic functions and integrals On the pseudo-periods of the Weierstrass zeta functions. II
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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 Dirac operator; Laplacian operator; twisted boundary conditions Russo, R.; Sciuto, S., Twisted determinants on higher genus Riemann surfaces, Nucl. Phys., B 669, 207, (2003) Quantum field theory on curved space or space-time backgrounds, Selfadjoint operator theory in quantum theory, including spectral analysis, Riemann surfaces; Weierstrass points; gap sequences, Theta functions and curves; Schottky problem Twisted determinants on higher genus 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 Riemann surfaces, Teichmüller theory for Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Hyperelliptische Riemannsche Flächen: Automorphismengruppen, Überlagerungen und Teichmüllerräume. (Hyperelliptic Riemann surfaces: automorphism groups, coverings and Teichmüller spaces)
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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 matrix models; two dimensional gravity; intersection theory of the moduli space of Riemann surfaces; Schur functions Di Francesco P., Itzykson C., Zuber J.-B.: Polynomial averages in the Kontsevich model. Commun. Math. Phys. 151, 193--219 (1993) Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, String and superstring theories in gravitational theory Polynomial averages in the Kontsevich model
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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 Ishii, N., The Weierstrass gap sets for quadruples II, Bull. Braz. Math. Soc. (N.S.), 42, 243-258, (2011) Riemann surfaces; Weierstrass points; gap sequences The Weierstrass gap sets for quadruples. II
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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 of the rational function fields Brauer groups of schemes, Galois cohomology, Arithmetic theory of algebraic function fields Groupe de Brauer des corps de fractions rationnelles à coefficients complexes
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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 Laurent expansions; compact Riemann surface; string theory Klimek, S., and Lesniewski, A. Global Laurent expansions on Riemann surfaces.Commun. Math. Phys. 125, 597--611 (1989). Differentials on Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Global Laurent expansions on 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 supersymmetry and duality; brane dynamics in gauge theories; supersymmetric effective theories; D-branes Benini, F.; Tachikawa, Y.; Xie, D., Mirrors of 3\(D\) Sicilian theories, JHEP, 09, 063, (2010) Yang-Mills and other gauge theories in quantum field theory, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Supersymmetric field theories in quantum mechanics, Riemann surfaces; Weierstrass points; gap sequences, Mirror symmetry (algebro-geometric aspects) Mirrors of 3d Sicilian theories
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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 automorphism of a Klein surface; period matrix; group of automorphisms Riera, J. London Math. Soc. 51 pp 442-- (1995) Riemann surfaces; Weierstrass points; gap sequences, Birational automorphisms, Cremona group and generalizations Automorphisms of abelian varieties associated with Klein 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 function fields; curves of genus greater than 1; finite number of points defined over the ground field Curves of arbitrary genus or genus \(\ne 1\) over global fields, Arithmetic theory of algebraic function fields, Rational points Diophantine equations over 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 Riemann surface; moduli space; algebraic curve; tropical curve; tropical moduli; Teichmüller space Research exposition (monographs, survey articles) pertaining to algebraic geometry, Families, moduli of curves (analytic), Riemann surfaces; Weierstrass points; gap sequences, Relationships between algebraic curves and physics, Classification theory of Riemann surfaces, Geometric group theory Introduction to moduli spaces of Riemann surfaces and tropical 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 Arakelov-Green function; delta-invariant; Weierstrass point de Jong R.: Arakelov invariants of Riemann surfaces. Doc. Math. 10, 311--329 (2005) Arithmetic varieties and schemes; Arakelov theory; heights, Theta functions and curves; Schottky problem, Riemann surfaces; Weierstrass points; gap sequences Arakelov invariants of 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 Krichever-Novikov algebras; Witt algebra; deformations; rigidity Lie algebras of vector fields and related (super) algebras, Formal methods and deformations in algebraic geometry, Elliptic curves, Riemann surfaces; Weierstrass points; gap sequences, Homological methods in Lie (super)algebras, Virasoro and related algebras Global deformations of Lie algebras
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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 reciprocity law for surfaces over finite fields; group of degree 0 zero- cycles; rational equivalence; abelian geometric fundamental group; unramified class field theory; K-theory; Chow groups Jean-Louis Colliot-Thélène & Wayne Raskind, ``On the reciprocity law for surfaces over finite fields'', J. Fac. Sci. Univ. Tokyo Sect. IA Math.33 (1986) no. 2, p. 283-294 Finite ground fields in algebraic geometry, Coverings in algebraic geometry, Algebraic cycles, Parametrization (Chow and Hilbert schemes), Homotopy theory and fundamental groups in algebraic geometry, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Arithmetic theory of algebraic function fields On the reciprocity law for surfaces 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 \((t,s)\)-sequences; \((t,m,s)\)-nets; survey; orthogonal latin squares; orthogonal array; rational points; algebraic-geometric codes; bounds; curves over a finite field Harald Niederreiter, Nets, (\?,\?)-sequences, and algebraic curves over finite fields with many rational points, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), 1998, pp. 377 -- 386. Pseudo-random numbers; Monte Carlo methods, Curves over finite and local fields, Orthogonal arrays, Latin squares, Room squares, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory, Bounds on codes Nets, \((t,s)\)-sequences, and algebraic curves over finite fields with many rational 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 limits of Weierstrass points; degeneration to stable curves; family of curves E. Esteves and N. Medeiros, Limit canonical systems on curves with two components, Inventiones Mathematicae 149 (2002), 267--338. Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic) Limit canonical systems on curves with two components
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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; Wronskian and compact Riemann surfaces Riemann surfaces; Weierstrass points; gap sequences A note on extremal compact 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 specialization of Galois extensions; function fields; Chebotarev property; Hilbert's irreducibility theorem; local and global fields Checcoli, S.; Dèbes, P.: Tchebotarev theorems for function fields. (2013) Arithmetic theory of algebraic function fields, Separable extensions, Galois theory, Hilbertian fields; Hilbert's irreducibility theorem, Field arithmetic, Arithmetic problems in algebraic geometry; Diophantine geometry Tchebotarev theorems 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 separable algebraic function field; s-subfield; unique maximal s- subfield; inequality of Castelnuovo; hyperelliptic function field H. Stichtenoth, s-Erweiterungen algebraischer Funktionenkörper. Arch. Math. 43, 27--31 (1984). Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group s-Erweiterungen algebraischer Funktionenkörper
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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 Macbeath curve; Weierstrass points Special algebraic curves and curves of low genus, Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences Weierstrass points on Macbeath's 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 of one variable; algebraic function fields; arbitrary field of constants Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Fields of algebraic functions of one variable over an arbitrary field of 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 principal bundles over algebraic curves; semistability of principal bundles; Jordan-Hölder theorem Ramanathan, A., \textit{Moduli for principal bundles over algebraic curves. II}, Proc. Indian Acad.Sci. Math. Sci. 106 (1996), no. 4, 421--449. Algebraic moduli problems, moduli of vector bundles, Vector bundles on curves and their moduli, Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences Moduli for principal bundles over algebraic curves. II
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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 Curves; Riemann surfaces Differentials on Riemann surfaces, Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences A basis of the space of meromorphic differentials on 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 defect of the valued function fields; genus; ramification index Michel Matignon, Genre et genre résiduel des corps de fonctions valués, Manuscripta Math. 58 (1987), no. 1-2, 179 -- 214 (French, with English summary). Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Ramification problems in algebraic geometry, Valued fields Genre et genre residuel des corps de fonctions valués. (Genus and residual genus of valued 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 Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Riemann surface with cyclic automorphisms group.
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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 limit of ramification points; nodal curves Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences Limit Weierstrass points on nodal reducible 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 Extremal Riemann surfaces; Riemann surfaces; Proceedings; Special sesseion; San Francisco, CA (USA) Quine, J.R., Sarnak, P. (eds.): Extremal Riemann surfaces, Contemporary Mathematics, 201. AMS (1997) Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to functions of a complex variable, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to global analysis, Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Partial differential equations on manifolds; differential operators Extremal Riemann surfaces. From the proceedings of the AMS special session with related papers, January 4--5, 1995, San Francisco, CA, USA
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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; Klein surface; Real form; Automorphism group Bujalance, E., Cirre F. J. and Turbek, P.: Riemann surfaces with real forms which have maximal cyclic symmetry. J. Algebra 283 (2005), no. 2, 447-456. Klein surfaces, Riemann surfaces; Weierstrass points; gap sequences, Topology of real algebraic varieties Riemann surfaces with real forms which have maximal cyclic symmetry
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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; compact Riemann surface; generalized theta bundle; Verlinde formula; conformal quantum field; representation theory of Kac-Moody algebras A. Beauville and Y. Laszlo, ''Conformal blocks and generalized theta functions,'' Comm. Math. Phys., vol. 164, iss. 2, pp. 385-419, 1994. Theta functions and curves; Schottky problem, Vector bundles on curves and their moduli, Quantum field theory on curved space or space-time backgrounds, Theta functions and abelian varieties, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Riemann surfaces; Weierstrass points; gap sequences Conformal blocks and generalized theta 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 multiple points; ramification points; gonal curves; Weierstrass sets Special divisors on curves (gonality, Brill-Noether theory), Riemann surfaces; Weierstrass points; gap sequences Weierstrass multiple points and ramification points of smooth 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 plane curves; one place at infinity; semigroup criterion; approximate roots M. Suzuki, ''Affine plane curves with one place at infinity,'' Ann. Inst. Fourier (Grenoble) 49(2), 375--404 (1999). Special algebraic curves and curves of low genus, Embeddings in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences Affine plane curves with one place at infinity
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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 ramification index; Puiseux expansions; algebraic function; algorithm David Lee Hilliker, An algorithm for computing the values of the ramification index in the Puiseux series expansions of an algebraic function, Pacific J. Math. 118 (1985), no. 2, 427 -- 435. Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry An algorithm for computing the values of the ramification index in the Puiseux series expansions of an algebraic function
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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 real holomorphic functions; compact connected Riemann surface; number of monodromy graphs DOI: 10.1016/S0166-8641(98)00084-4 Real algebraic sets, Enumeration in graph theory, Relations of low-dimensional topology with graph theory, Structure of families (Picard-Lefschetz, monodromy, etc.), Riemann surfaces; Weierstrass points; gap sequences Monodromies of generic real 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 Riemann--Hilbert problem; Fuchsian equation; dessins d'enfants Lárusson, F.; Sadykov, T., Dessins d'enfants and differential equations, Algebra Anal., 19, 184-199, (2007) Riemann surfaces; Weierstrass points; gap sequences, Discrete version of topics in analysis, Classical hypergeometric functions, \({}_2F_1\), Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain Dessins d'enfants and differential 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 Theta-functions; Riemann surfaces; prime form; sigma function Gibbons, J., Matsutani, S., Ônishi, Y.: Relationship between the prime form and the sigma function for some cyclic \((r, s)\) curves. J. Phys. A \textbf{46}(17), 175203, 21 pp (2013) Theta functions and abelian varieties, Riemann surfaces; Weierstrass points; gap sequences, Representations of finite symmetric groups, Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems Relationship between the prime form and the sigma function for some cyclic (\(r, s\)) 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 curvature; Milnor fibre Riemann surfaces; Weierstrass points; gap sequences, Milnor fibration; relations with knot theory A'Campo curvature bumps and the Dirac phenomenon near a singular point
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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 smooth Weierstrass points; nodal curve Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings On the distribution of Weierstrass points on irreducible rational 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 moduli spaces of curves; gap sequences; SINGULAR Nakano, T.; Mori, T., On the moduli space of pointed algebraic curves of low genus--A computational approach, Tokyo J. Math., 27, 239-253, (2004) Families, moduli of curves (algebraic), Computational aspects in algebraic geometry, Riemann surfaces; Weierstrass points; gap sequences On the moduli space of pointed algebraic curves of low genus: a computational approach
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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 \(3\)-Weierstrass points Farahat, Mohamed; Sakai, Fumio, The 3-Weierstrass points on genus two curves with extra involutions, Saitama Math. J., 28, 1-12 (2012), (2011) Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus The 3-Weierstrass points on genus two curves with extra involutions
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