Transcendence in positive characteristic and special values of hypergeometric functions
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Abstract
We prove a simple transcendence criterion suitable for function field arithmetic. We apply it to show the transcendence of special values at non-zero rational arguments (or more generally, at algebraic arguments which generate extension of the rational function field with less than q places at infinity) of the entire hypergeometric functions in the function field (over 𝔽q) context, and to obtain a new proof of the transcendence of special values at non-natural p-adic integers of the Carlitz–Goss gamma function. We also characterize in the balanced case the algebraicity of hypergeometric functions, giving an analog of the result of F. R. Villegas, based on Beukers–Heckman results and E. Landau's method in the classical hypergeometric case.
© Walter de Gruyter Berlin · New York 2011
Articles in the same Issue
- Coefficients and non-triviality of the Jones polynomial
- Distribution of algebraic numbers
- Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs
- Characterizing quaternion rings over an arbitrary base
- Transcendence in positive characteristic and special values of hypergeometric functions
- Factoring 3-fold flips and divisorial contractions to curves
- Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
- -actions on UHF algebras of infinite type
Articles in the same Issue
- Coefficients and non-triviality of the Jones polynomial
- Distribution of algebraic numbers
- Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs
- Characterizing quaternion rings over an arbitrary base
- Transcendence in positive characteristic and special values of hypergeometric functions
- Factoring 3-fold flips and divisorial contractions to curves
- Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
- -actions on UHF algebras of infinite type
