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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 sigma function; affine space curve; Weierstrass semigroup Matsutani, Shigeki and Komeda, Jiryo, Sigma functions for a space curve of type {\((3,4,5)\)}, Journal of Geometry and Symmetry in Physics, 30, 75-91, (2013) Riemann surfaces; Weierstrass points; gap sequences Sigma functions for a space curve of type \((3, 4, 5)\)
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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 simple closed geodesics Kuusalo, T.; Näätänen, M., Weierstrass points of genus-2 surfaces with regular fundamental domains, Quart. J. Math., 54, 355, (2003) Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Weierstrass points of genus-2 surfaces with regular fundamental domains
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic geometric codes; towers of function fields Geometric methods (including applications of algebraic geometry) applied to coding theory, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Applications to coding theory and cryptography of arithmetic geometry Integral bases in a tower 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 point; gap sequence; coarse moduli space M. COPPENS, Weierstrass points on trigonal curves I : The ramification points, Preprint R. U. Utrecht, 430 (1986) Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Algebraic moduli problems, moduli of vector bundles Weierstrass points on trigonal curves. I: The ramification 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 Ullrich-Selberg's ramification; theorem; discriminant; meromorphic functions; Picard exceptional values M. OZAWA AND K. SAWADA, Picard constants of four-sheeted algebroid surfaces, I, Kodai Math. J., 18 (1995), 99-141. Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Riemann surfaces; Weierstrass points; gap sequences, Riemann surfaces Picard constants of four-sheeted algebroid surfaces. I
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic conformal blocks; Knizhnik-Zamolodchikov equations; WZW-model; moduli spaces G. Felder, ''The KZB equations on Riemann surfaces,'' in: Symétries Quantiques (Les Houches, 1995), North-Holland, Amsterdam (1998), pp. 687-725; arXiv:hep-th/9609153v1 (1996). Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Riemann surfaces; Weierstrass points; gap sequences, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Applications of Lie (super)algebras to physics, etc., Lie algebras of vector fields and related (super) algebras, Moduli problems for differential geometric structures The KZB equations 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 Galois point; genus; quartic curve Watanabe S.: The genera of Galois closure curves for plane quartic curve. Hiroshima Math. J. 38, 125--134 (2008) Riemann surfaces; Weierstrass points; gap sequences, Algebraic functions and function fields in algebraic geometry The genera of Galois closure curves for plane quartic 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 Carlitz module; transcendence of \(\pi \); Carlitz zeta function J.-P. Allouche, Sur la transcendance de la série formelle \(\Pi\), Journal de Théorie des Nombres de Bordeaux 2 (1990), 103-117. | Arithmetic theory of algebraic function fields, Transcendence (general theory), Arithmetic theory of polynomial rings over finite fields, Finite ground fields in algebraic geometry Sur la transcendance de la série formelle \(\Pi\) . (On the transcendence of formal power series \(\Pi\) )
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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 quantized point vortex theories; strings; Riemann surface; Riemann-Roch theorems 38.V. Penna, M. Spera, Remarks on quantum vortex theory on Riemann surfaces. J. Geom. Phys. 27, 99-112 (1998) Relationships between algebraic curves and physics, Geometry and quantization, symplectic methods, Riemann surfaces; Weierstrass points; gap sequences, Riemann-Roch theorems, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Statistical mechanics of superfluids Remarks on quantum vortex theory on Riemann surfaces. -- Appendix A. An application: Vortices on an elliptic 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 genus of a Riemann surface; generalised Castelnuovo curves; linear series Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization Generalized Castelnuovo inequalities
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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 Mumford curves; trees; harmonic measures on trees; non-Archimedean analysis; Schottky group; canonical embeddings of curves; holomorphic forms Gunther Cornelissen and Janne Kool.Rigidity and reconstruction for graphs. Preprint arXiv:1601.08130(2016), 9 pp. Rigid analytic geometry, Non-Archimedean analysis, Dynamical systems over non-Archimedean local ground fields, Abstract harmonic analysis, Groups acting on trees, Arithmetic varieties and schemes; Arakelov theory; heights, Riemann surfaces; Weierstrass points; gap sequences Measure-theoretic rigidity for Mumford 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 Laurent polynomial; Minkowski sum; Newton polytope Toric varieties, Newton polyhedra, Okounkov bodies, Plane and space curves, Riemann surfaces; Weierstrass points; gap sequences Bivariate systems of polynomial equations with roots of high multiplicity
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic hyperelliptic curves; superelliptic curves; Weierstrass points Shor, C.; Shaska, T., Weierstrass points of superelliptic curves.Advances on superelliptic curves and their applications, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur. 41, 15-46, (2015), IOS, Amsterdam Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Coverings of curves, fundamental group Weierstrass points of 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 points; automorphism of compact Riemann surface Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences Weierstrass points of weight 3 and fixed points of automorphisms of 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 function field of one variable over a finite field; group of divisor classes; upper bound; zeta-function Arithmetic theory of algebraic function fields, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry Divisorklassen der Ordnung \(\ell\) bei Kongruenzfunktionenkörpern
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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 of genus three: moduli space; Weierstrass point; Cartier operator Special algebraic curves and curves of low genus, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic), Theta functions and curves; Schottky problem The moduli of certain curves of genus three in characteristic two
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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 p-adic field; liftings; coverings of a curve over a finite field Arithmetic ground fields for curves, Coverings of curves, fundamental group, Finite ground fields in algebraic geometry, Arithmetic theory of algebraic function fields, Local ground fields in algebraic geometry On the ramified congruence relations of algebraic 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 point; Weierstrass weight; non-hyperelliptic Riemann surfaces of genus five Horiuchi R.: Non-hyperelliptic Riemann surfaces of genus five all of whose Weierstrass points have maximal weight. Kodai Math. J. 30, 379--384 (2007) Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Special algebraic curves and curves of low genus Non-hyperelliptic Riemann surfaces of genus five all of whose Weierstrass points have maximal weight
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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; algebraic curve; Hurwitz curve; automorphism; Jacobians Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Automorphisms of curves, Jacobians, Prym varieties About the Fricke-Macbeath 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 quotient surface; abelian function field; abelian surface Cantat, S., Favre, C.: Symétries birationnelles des surfaces feuilletées. J. Reine Angew. Math. \textbf{561}, 199-235 (2003) [Corrigendum à l'article ''Symétries birationnelles des surfaces feuilletées''. J. Reine Angew. Math. \textbf{582}, 229-231 (2005)] Abelian varieties and schemes, Homogeneous spaces and generalizations, Families, moduli, classification: algebraic theory, Arithmetic ground fields for surfaces or higher-dimensional varieties, Arithmetic theory of algebraic function fields Quotients of abelian 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 Pythagoras number; real domain; formal power series; numerical semigroup; curves with a given semigroup Ortega J. (1991). On the Pythagoras number of a real irreducible algebroid curve. Math. Ann. 289: 111--123 Real algebraic sets, Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), Formal power series rings, Riemann surfaces; Weierstrass points; gap sequences, Sums of squares and representations by other particular quadratic forms On the Pythagoras number of a real irreducible algebroid 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 string theory; string amplitudes; higher genus; handle operators String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Fine and coarse moduli spaces, Path integrals in quantum mechanics, Riemann surfaces; Weierstrass points; gap sequences, Vertex operators; vertex operator algebras and related structures, Feynman diagrams, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations Handle operators in string 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 hyperelliptic integrals; differential equations in the complex domain Riemann surfaces; Weierstrass points; gap sequences, Differentials on Riemann surfaces, General theory for ordinary differential equations The module of periods of the hyperelliptic integrals considered as a function of a parameter.
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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 hyperbolic Riemann surfaces; systole; principal ``congruence'' subgroups of a fixed arithmetic subgroup; regular graphs Makisumi, S., A note on Riemann surfaces of large systole, J. Ramanujan Math. Soc., 28, 359-377, (2013) Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Riemann surfaces; Weierstrass points; gap sequences A note on Riemann surfaces of large systole
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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 canonically embedded curve; algebraic monodromy; rational scroll; Weierstrass point Canuto C.,On the monodromy of Weierstrass points, Annali di Matematica pura ed appl.136 (1984), 49--63. Riemann surfaces; Weierstrass points; gap sequences, Curves in algebraic geometry, Coverings in algebraic geometry On the monodromy of 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 composite rational function; lacunary polynomial Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry On composite rational 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 gap sequence; general nodal curve; Weierstraß points; weight Lax, R. F.: Weierstraß points on rational nodal curves,Glasgow Math. J. 29 (1987), no. 1, 131-140. Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings, Rational and unirational varieties Weierstrass points on 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 Klein surfaces; finite group actions; full real genus Klein surfaces, Riemann surfaces; Weierstrass points; gap sequences Extensions of finite cyclic group actions on bordered 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 Diffie-Hellman key exchange; discrete logarithm problem; real quadratic congruence function fields; elliptic curves Andreas Stein, Equivalences between elliptic curves and real quadratic congruence function fields, J. Théor. Nombres Bordeaux 9 (1997), no. 1, 75 -- 95 (English, with English and French summaries). Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects), Cryptography, Number-theoretic algorithms; complexity, Elliptic curves over global fields, Elliptic curves Equivalences between elliptic curves and real quadratic congruence function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic curve; \(L\)-function; quadratic twist; rational function; sum of \(L\)-functions B. Fisher and S. Friedberg, Double Dirichlet series over function fields, Compositio Mathematica 140 (2004), 613--630. Zeta and \(L\)-functions in characteristic \(p\), Curves over finite and local fields, Gauss and Kloosterman sums; generalizations, Estimates on exponential sums, Other analytic theory, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Double Dirichlet series 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 curves of low genus; quadratic sequences; Mohanty's conjecture; function field arithmetic Higher degree equations; Fermat's equation, Rational points, Arithmetic theory of algebraic function fields Quadratic sequences of powers and Mohanty's conjecture
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic generalized Weierstrass semigroups; Riemann-Roch spaces; Poincaré Riemann surfaces; Weierstrass points; gap sequences, Finite ground fields in algebraic geometry, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series Generalized Weierstrass semigroups and their Poincaré series
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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 character theory Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences, Ordinary representations and characters The character theory of groups and automorphism groups of Riemann surfaces. I
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic supermoduli spaces; superstrings; deformations of supercurves Falqui, G., Reina, C.: Supermoduli and Superstrings. In: Proceedings of the C.I.M.E. Summer Course ''Global Geometry and Mathematical Physics'', Montecattini, Italy, July 1988 Families, moduli of curves (algebraic), Complex supergeometry, Supervarieties, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Riemann surfaces; Weierstrass points; gap sequences Supermoduli and superstrings
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic number of isomorphism classes of principally polarized abelian varieties; complex multiplication; ideal class number; Jacobian varieties of compact Riemann surfaces Riera, G.; Rodríguez, Rubí E., Riemann surfaces and abelian varieties with an automorphism of prime order, Duke Math. J., 69, 199-217, (1993) Complex multiplication and abelian varieties, Riemann surfaces; Weierstrass points; gap sequences, Jacobians, Prym varieties Riemann surfaces and abelian varieties with an automorphism of prime order
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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 quadric curve; gaps; complete intersection curves; Cohen-Macaulay curves; Buchsbaum curves; Lüroth semigroup DOI: 10.1007/BF02567082 Riemann surfaces; Weierstrass points; gap sequences, Divisors, linear systems, invertible sheaves On the Lüroth semigroup of curves lying on a smooth quadric
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Diophantine approximation; Chow-forms Ferretti, R G, Diophantine approximations and toric deformations, Duke Math J, 118, 493-522, (2003) Diophantine inequalities, Results involving abelian varieties, Arithmetic varieties and schemes; Arakelov theory; heights, Toric varieties, Newton polyhedra, Okounkov bodies Diophantine approximations and toric deformations
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic k-Weierstrass points; family of compact Riemann surfaces; Teichmüller space Pflaum, U., Vollständige Invarianten der Biholomorphieklassen kompakter Riemannscher Flächen mit Hilfe höherer Weierstrasspunkte, Dissertation. Duisburg (1985) Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Special algebraic curves and curves of low genus, Families, moduli of curves (analytic) Vollständige Invarianten der Biholomorphieklassen kompakter Riemannscher Flächen mit Hilfe höherer Weierstrasspunkte. (Complete invariants of the classes of biholomorphy of compact Riemann surfaces via higher 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 Riemann surfaces; Weierstrass points; gap sequences Invariant spin structures 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 toric surface; smooth curve; Weierstrass semigroup; numerical semigroup; MP equalities; cyclic covering Riemann surfaces; Weierstrass points; gap sequences, Toric varieties, Newton polyhedra, Okounkov bodies, Coverings of curves, fundamental group, Special divisors on curves (gonality, Brill-Noether theory), Commutative semigroups Weierstrass semigroups satisfying MP equalities and curves on toric 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 Weierstrass points; curves of low genus; double covering; elliptic involution Keem, C; Martens, G, On curves with all Weierstrass points of maximal weight, Arch. Math., 94, 339-349, (2010) Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus On curves with all Weierstrass points of maximal weight
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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; maximal curves; AG codes Sepúlveda, A; Tizziotti, G, Weierstrass semigroup and codes over the curve \(y^q + y = x^{q^r} + 1\), Adv. Math. Commun., 8, 67-72, (2014) Riemann surfaces; Weierstrass points; gap sequences, Curves over finite and local fields, Heights Weierstrass semigroup and codes over the curve \(y^q + y = x^{q^r + 1}\)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic diophantine approximation; G-functions; algebraic functions; Hilbert's irreducibility theorem; height on abelian varieties Dèbes, P.: G-fonctions et théorème d'irréductibilité de Hilbert. Acta arith. 47 (1986) Hilbertian fields; Hilbert's irreducibility theorem, Transcendence theory of other special functions, Heights, Polynomials (irreducibility, etc.), Arithmetic theory of algebraic function fields, Global ground fields in algebraic geometry \(G\)-functions and Hilbert's irreducibility 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 algebraic function field; Kummer extension; genus field; Hilbert extension Peng G.: The genus fields of Kummer function fields. J. Number Theory 98, 221--227 (2003) Other abelian and metabelian extensions, Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry The genus fields of Kummer 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 global function fields; curves with many rational points Arithmetic theory of algebraic function fields, Curves over finite and local fields, Finite ground fields in algebraic geometry, Rational points Global function fields with many rational places over the quinary 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 compact Riemann surfaces; automorphism groups Carocca, A.; González-Aguilera, V.; Hidalgo, R. A.; Rodriguez, R., Generalized Humbert curves, Isr. J. Math., 164, 1, 165-192, (2008) Classification theory of Riemann surfaces, Families, moduli of curves (algebraic), Riemann surfaces; Weierstrass points; gap sequences, Automorphisms of curves, Compact Riemann surfaces and uniformization Generalized Humbert 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 non-gap sequences; trigonal covering; trigonal curve [Ki] Kim, S.J.: On the Existence of Weierstrass Gap Sequences on Trigonal Curves, J. Pure Appl. Algebra, 63 (1990), 171--180 Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Compact Riemann surfaces and uniformization, Divisors, linear systems, invertible sheaves On the existence of Weierstrass gap sequences on trigonal curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Weierstrass semigroup of a point; double covering of a curve; cyclic covering of an elliptic curve DOI: 10.1007/s00574-008-0074-5 Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group, Divisors, linear systems, invertible sheaves Existence of the non-primitive Weierstrass gap sequences on curves of genus 8
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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 Drinfeld modules; elliptic modules; cyclotomic function fields; congruence function fields; Carlitz modules; nonarchimedean analysis; explicit class field theory; Gauss sums; Gamma and Zeta functions and values; Jacobi sums; diophantine approximation; \(t\)-modules; \(t\)-motives; transcendence and irrationality; automata and algebraicity D.S. Thakur, \(Function Field Arithmetic\), World Scientfic, Singapore, 2004. Research exposition (monographs, survey articles) pertaining to number theory, Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Curves over finite and local fields, Transcendence (general theory), Zeta and \(L\)-functions in characteristic \(p\), Class field theory, Other character sums and Gauss sums, Arithmetic theory of polynomial rings over finite fields, Arithmetic ground fields (finite, local, global) and families or fibrations, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Arithmetic ground fields for curves Function field arithmetic
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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 coding theory; algebraic geometry; algebraic curves; algebraic number theory; error-correcting codes; curves over finite fields Tsfasman M., Vlăduţ S., Nogin D.: Algebraic Geometric Codes: Basic Notions, vol. 139. Math. Surv. Monogr.Amer. Math. Soc., Providence, RI (2007). Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory, Theory of error-correcting codes and error-detecting codes, Applications to coding theory and cryptography of arithmetic geometry, Curves in algebraic geometry, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Algebraic coding theory; cryptography (number-theoretic aspects) Algebraic geometric codes. Basic notions
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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 torsion points; jacobian variety; Albanese morphism; Weierstrass points Tamagawa, A., Ramification of torsion points on curves with ordinary semistable Jacobian varieties. Duke Math. J. 106 (2001), 281-319. Zbl1010.14007 MR1813433 Jacobians, Prym varieties, Riemann surfaces; Weierstrass points; gap sequences, Arithmetic aspects of modular and Shimura varieties, Arithmetic ground fields for curves, Modular and Shimura varieties Ramification of torsion points on curves with ordinary semistable Jacobian varieties
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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 A note on weights of 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 compact Riemann surfaces; holomorphic vector bundles; logarithmic connections; quasi-fuchsian logarithmic connection; Riemann-Hilbert problem C. Gantz and B. Steer, ''Gauge fixing for logarithmic connections over curves and the Riemann--Hilbert problem,'' J. London Math. Soc. (2), 59, No. 2, 479--490 (1999). Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Vector bundles on curves and their moduli Gauge fixing for logarithmic connections over curves and the Riemann-Hilbert problem
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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 tame algebras; symmetric special biserial algebras; gentle algebras; trivial extensions; Brauer graph algebras; admissible cuts; marked Riemann surfaces; triangulations Schroll, S., Trivial extensions of gentle algebras and Brauer graph algebras, J. Algebra, 444, 183-200, (2015) Representations of quivers and partially ordered sets, Representation type (finite, tame, wild, etc.) of associative algebras, Cluster algebras, Riemann surfaces; Weierstrass points; gap sequences, Representations of associative Artinian rings Trivial extensions of gentle algebras and Brauer graph 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 finite Galois coverings; closed Riemann surfaces; complex manifolds , Finite branched coverings of complex manifolds, Sugaku Expositions 5 (1992), no. 2, 193-211. Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Coverings in algebraic geometry, Coverings of curves, fundamental group Finite branched coverings of complex manifolds
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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 Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 1996. Rational points, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Elliptic curves over global fields, Elliptic curves Mordell-Weil groups in procyclic extensions 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 integral polynomial; splitting field; specialization Polynomials (irreducibility, etc.), Galois theory, Arithmetic theory of algebraic function fields, Rational points Arithmetic specializations in the splitting fields of polynomials
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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 points; Diophantine approximation; Schmidt's subspace theorem; Vojta's main conjecture Schmidt Subspace Theorem and applications, Global ground fields in algebraic geometry, Diophantine inequalities, Curves of arbitrary genus or genus \(\ne 1\) over global fields, Rational points, Heights On arithmetic inequalities for points of bounded degree
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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 linearized polynomial; permutation polynomial; maximal curve; finite fields Özbudak, Ferruh: On maximal curves and linearized permutation polynomials over finite fields, J. pure appl. Algebra 162, No. 1, 87-102 (2001) Curves over finite and local fields, Arithmetic theory of algebraic function fields, Polynomials over finite fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Arithmetic ground fields for curves On maximal curves and linearized permutation polynomials 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 special divisor; double covering; hyperelliptic curve; small Clifford index Divisors, linear systems, invertible sheaves, Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group A special divisor on a double covering 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 Gál's sums; Dirichlet polynomials; Riemann zeta function; Dirichlet \(L\)-functions; resonance method; function fields Zeta functions and \(L\)-functions of function fields, \(\zeta (s)\) and \(L(s, \chi)\), Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Large values of Dirichlet \(L\)-functions 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; modular group; congruence subgroups; Veech groups of origamis Weitze-Schmithüsen, G.: The deficiency of being a congruence group for Veech groups of origamis. Int. Math. Res. Not. \textbf{2015}(6), 1613-1637 (2015) Compact Riemann surfaces and uniformization, Fuchsian groups and their generalizations (group-theoretic aspects), Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Teichmüller theory for Riemann surfaces, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Riemann surfaces; Weierstrass points; gap sequences The deficiency of being a congruence group for Veech groups of origamis
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic higher \(K\)-theory; hyperelliptic Jacobian; Jacobian variety; Quillen group; Griffiths' infinitesimal invariant Collino, A., Griffiths' infinitesimal invariant and higher \(K\)-theory on hyperelliptic Jacobians, J. Alg. Geom. 6 (1997), 393-415. Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Algebraic cycles, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Jacobians, Prym varieties, Riemann surfaces; Weierstrass points; gap sequences Griffiths' infinitesimal invariant and higher \(K\)-theory on hyperelliptic Jacobians
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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 Artin-Schreier extension; compositum; decomposition law; different; ramification group Wu, Q.; Scheidler, R., The ramification groups and different of a compositum of Artin-Schreier extensions, Int. J. Number Theory, 6, 1541-1564, (2010) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Other abelian and metabelian extensions, Special algebraic curves and curves of low genus The ramification groups and different of a compositum of 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 Weierstrass points; modular curve; hyperelliptic curve Riemann surfaces; Weierstrass points; gap sequences, Arithmetic aspects of modular and Shimura varieties Weierstrass points on hyperelliptic modular 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 hyperelliptic curve cryptography; explicit formulae; Kummer surface; theta functions Oliveira, G., Pimentel, F.L.R.: On Weierstrass semigroups of double covering of genus two curves. Semigroup Forum 77, 152--162 (2008) Riemann surfaces; Weierstrass points; gap sequences On Weierstrass semigroups of double covering of genus two curves
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Theta functions; Abelian integrals; periods; Riemann surface; algebraic curves; characteristics; transformation theory. Theta functions and curves; Schottky problem, Riemann surfaces; Weierstrass points; gap sequences, Analytic theory of abelian varieties; abelian integrals and differentials Abel's theorem and the allied theory including the theory of the 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 Riemann surface; Riemann-Roch theorem; index of speciality Riemann surfaces; Weierstrass points; gap sequences On the theorem of Riemann-Roch. Note.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Algebraic curves; Algebraic functions of one variable Algebraic functions and function fields in algebraic geometry, Plane and space curves, Riemann surfaces; Weierstrass points; gap sequences Algebraic functions considered geometrically.
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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 Drinfeld module; Drinfeld modular curve; Ihara's quantity; BBGS tower Drinfel'd modules; higher-dimensional motives, etc., Arithmetic theory of algebraic function fields, Computational aspects of algebraic curves, Algebraic functions and function fields in algebraic geometry A modular interpretation of BBGS towers
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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 surface; \(z _{ n }\) curve; nonspecial integral divisor; theta functions; Abel-Jacobi map; \(\lambda \)-function Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Compact complex surfaces, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Generalizations of Hutchinson's curve and the Thomae formulae
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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 multiple zeta values; Furusho conjecture Arithmetic theory of algebraic function fields, Transcendence theory of Drinfel'd and \(t\)-modules, Generalizations (algebraic spaces, stacks), Formal groups, \(p\)-divisible groups, Finite ground fields in algebraic geometry On a conjecture of Furusho 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 composite rational functions; lacunary polynomials; arithmetic progressions Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Composite rational functions and arithmetic progressions
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic algebraic curves; morphisms; semigroups Oliveira, G., Torres, F., Villanueva, J.: On the weight of numerical semigroups. J. Pure Appl. Algebra 214, 1955--1961 (2010) Riemann surfaces; Weierstrass points; gap sequences, Special algebraic curves and curves of low genus, Plane and space curves On the weight of numerical semigroups
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic Combinatorial aspects of tropical varieties, Riemann surfaces; Weierstrass points; gap sequences, Applications of graph theory, Commutative semigroups Weierstrass sets on finite graphs
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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 dessins d'enfants; bipartite maps; representation of the Galois group Riemann surfaces; Weierstrass points; gap sequences, Designs and configurations, Inverse Galois theory, Arithmetic ground fields for curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Dessins d'enfants: bipartite maps and Galois 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 elliptic curve; elliptic surface; function field; genus; gonality; \(p\)-rank; torsion; K3 surface Andreas Schweizer, On the \?^{\?}-torsion of elliptic curves and elliptic surfaces in characteristic \?, Trans. Amer. Math. Soc. 357 (2005), no. 3, 1047 -- 1059. Elliptic curves over global fields, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Elliptic curves, Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Global ground fields in algebraic geometry, \(K3\) surfaces and Enriques surfaces On the \(p^e\)-torsion of elliptic curves and elliptic surfaces in characteristic \(p\)
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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 de Rham cohomology; transcendency; function fields over a finite field; t-modules; Drinfeld modules; quasi-periodic functions; elliptic curve; special values; quasi-periods; Legendre formula Jing Yu, On periods and quasi-periods of Drinfel\(^{\prime}\)d modules, Compositio Math. 74 (1990), no. 3, 235 -- 245. Arithmetic theory of algebraic function fields, Drinfel'd modules; higher-dimensional motives, etc., de Rham cohomology and algebraic geometry, Elliptic curves over global fields On periods and quasi-periods 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 Weierstrass form; addition laws on an elliptic curve Bosma W, Lenstra Jr H W. Complete systems of two addition laws for elliptic curves[J]. Journal of Number Theory, 1995, 53: 229--240. Elliptic curves, Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves over global fields Complete systems of two addition laws for elliptic 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 subanalytic sets; parametrization; rational points of bounded height Real-analytic and semi-analytic sets, Applications of model theory, Diophantine equations Mild parametrizations of power-subanalytic sets
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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 groups; \(n\)-Brauer dimension; \(\mathbb Z/n\)-cyclic classes; \(\mathbb Z/n\)-lengths; connected regular projective relative curves; divisors; hot points; finitely-generated extensions of transcendence degree \(1\); Brauer equivalence classes of cyclic algebras; central division algebras E. Brussel and E. Tengan, Division algebras of prime period \( \ell \neq p\) over function fields of \( p\)-adic curves, Israel J. Math. (to appear). Finite-dimensional division rings, Curves over finite and local fields, Arithmetic theory of algebraic function fields, Skew fields, division rings, Local ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Brauer groups (algebraic aspects) Tame division algebras of prime period over function fields of \(p\)-adic 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 tensor powers of the Carlitz module; zeta values; motive; Tannakian category; conjectures of D. Zagier; multilogs; \(\zeta\)-functions of number fields Anderson, G.; Thakur, D., \textit{tensor powers of the Carlitz module and zeta values}, Ann. of Math. (2), 132, 159-191, (1990) Arithmetic theory of algebraic function fields, Drinfel'd modules; higher-dimensional motives, etc., Generalizations (algebraic spaces, stacks), Global ground fields in algebraic geometry, Formal groups, \(p\)-divisible groups, Applications of methods of algebraic \(K\)-theory in algebraic geometry Tensor powers of the Carlitz module and zeta values
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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 integrable Hamiltonian systems; Riemann surfaces Hurtubise, J., Separation of Variables and the Geometry of Jacobians, SIGMA Symmetry Integrability Geom. Methods Appl., 2007, vol. 3, Paper 017, 14 pp. (electronic). Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Riemann surfaces; Weierstrass points; gap sequences Separation of variables and the geometry of Jacobians
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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, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Cyclic groups of automorphisms of Schottky type.
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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 fibration over a compact Riemann surface; Fuchsian group; elliptic varieties; Hodge structures Transcendental methods, Hodge theory (algebro-geometric aspects), Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Riemann surfaces; Weierstrass points; gap sequences, Elliptic surfaces, elliptic or Calabi-Yau fibrations Hodge structures on parabolic cohomology
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations, Arithmetic theory of algebraic function fields, Riemann surfaces; Weierstrass points; gap sequences, Approximation in non-Archimedean valuations, Diophantine inequalities A note on Wronskians and the ABC theorem in function fields of prime characteristic symplectic form on the moduli space; Riemann surface; fundamental group Y Karshon, An algebraic proof for the symplectic structure of moduli space, Proc. Amer. Math. Soc. 116 (1992) 591 Homotopy theory and fundamental groups in algebraic geometry, Fine and coarse moduli spaces, Riemann surfaces; Weierstrass points; gap sequences, Families, moduli of curves (algebraic), General geometric structures on manifolds (almost complex, almost product structures, etc.) An algebraic proof for the symplectic structure of moduli 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 Klein surfaces; symmetric theta divisors; Appell-Humbert data; Yang-Mills connections; real vector bundles Riemann surfaces; Weierstrass points; gap sequences, Vector bundles on curves and their moduli, Jacobians, Prym varieties Symmetric theta divisors of 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 divisor of a differential; Gorenstein curve; desingularisation; ramification divisor; Weierstrass points on a singular curve De Carvalho, C. F.; Stöhr, K. -O.: Higher order differentials and Weierstrass points on Gorenstein curves. Manuscripta math. 85, 361-380 (1994) Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Divisors, linear systems, invertible sheaves Higher order differentials and Weierstrass points on Gorenstein 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 graph configurations; Dyck words Paths and cycles, Graph algorithms (graph-theoretic aspects), Graphs and abstract algebra (groups, rings, fields, etc.), Riemann surfaces; Weierstrass points; gap sequences On the ranks of configurations on the complete graph
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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 Clifford defect; geometric Goppa code; telescopic semigroup Decoding, Special algebraic curves and curves of low genus, Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences On the Clifford defect for special 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 of Riemann surfaces; Jacobian Riemann surfaces; Weierstrass points; gap sequences, Classification theory of Riemann surfaces, Rational points, Riemann surfaces 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 algebra, number theory Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Das arithmetische Geschlecht
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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 Morita-Mumford classes; mapping class groups; hyperelliptic curves; gap sequences; Bernoulli numbers DOI: 10.1016/S0166-8641(01)00272-3 General low-dimensional topology, Special algebraic curves and curves of low genus, Families, moduli of curves (analytic), Riemann surfaces; Weierstrass points; gap sequences Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class 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 elliptic and hyperelliptic curves; Jacobian variety; ruled and rational surfaces; exceptional curve; elliptic soliton Relationships between algebraic curves and integrable systems, Relationships between algebraic curves and physics, Soliton equations, KdV equations (Korteweg-de Vries equations), NLS equations (nonlinear Schrödinger equations), Coverings of curves, fundamental group, Jacobians, Prym varieties, Riemann surfaces; Weierstrass points; gap sequences, Divisors, linear systems, invertible sheaves, Soliton solutions Nonlinear evolution equations and hyperelliptic covers of elliptic 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 quasiplatonic surfaces; genus; subgroups of finite index; Fuchsian triangle groups; Riemann surfaces Schlage-Puchta, Jan-Christoph; Wolfart, Jürgen, How many quasiplatonic surfaces?, Arch. Math. (Basel), 86, 2, 129-132, (2006) Subgroup theorems; subgroup growth, Fuchsian groups and their generalizations (group-theoretic aspects), Discrete subgroups of Lie groups, Compact Riemann surfaces and uniformization, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Coverings of curves, fundamental group, Riemann surfaces; Weierstrass points; gap sequences, Asymptotic results on counting functions for algebraic and topological structures How many quasiplatonic 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 Weierstrass multiplicative point; Abel theorem; generalized theta function; Schottky group; Kleinian group; divisor; algebraic curve; modulus space; quasiconformal mapping; Riemann-Roch theorem V. V. Chueshev, \textit{Multiplicative Functions and Prym Differentials on a Variable Compact Riemann Surface} [in Russian], Kemerovo State Univ., Kemerovo (2003). Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, Jacobians, Prym varieties, Riemann surfaces; Weierstrass points; gap sequences, Differentials on Riemann surfaces, Compact Riemann surfaces and uniformization, Harmonic functions on Riemann surfaces, Teichmüller theory for Riemann surfaces, Vector bundles on curves and their moduli, Algebraic moduli problems, moduli of vector bundles, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) Multiplicative functions and Prym differentials on a variable compact Riemann surface. Part 2. Textbook
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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, Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory An optimal unramified tower 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 lower bounds; heights of solutions of linear equations in algebraic numbers Lower bounds for the heights of solutions of linear equations, Invent. Math. 129 (1997), 1--10. Approximation in non-Archimedean valuations, Heights, Approximation to algebraic numbers, Global ground fields in algebraic geometry Lower bounds for the heights of solutions of linear 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 Riemann surfaces; Weierstrass gap; holomorphic section Riemann surfaces; Weierstrass points; gap sequences Certain holomorphic sections relating to 2-pointed Weierstrass gap sets on 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 generalized Weierstrass point; Weierstrass semigroup of a pair; Weierstrass semigroup of a point Kang E., Kim S.J.: Special pairs in the generating subset of the Weierstrass semigroup at a pair. Geom. Dedicata 99, 167--177 (2003) Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization, Special divisors on curves (gonality, Brill-Noether theory), Applications to coding theory and cryptography of arithmetic geometry Special pairs in the generating subset of the Weierstrass semigroup at a pair
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