Gamma functions for function fields and Drinfeld modules

DOI10.2307/2944332zbMath0734.11036OpenAlexW2335130561MaRDI QIDQ810569

Dinesh S. Thakur

Publication date: 1991

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2944332

zbMATH Keywords

transcendencefunctional equationsspecial valuesperiodsalgebraicityinterpolationsgamma functionsDrinfel'd modules of rank onefunction fields of one variable

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Drinfel'd modules; higher-dimensional motives, etc. (11G09)

Related Items (29)

Linear independence of Gamma values in positive characteristic ⋮ Algebraic independence of arithmetic gamma values and Carlitz zeta values ⋮ A higher-dimensional analogue of Carlitz-Drinfeld theory ⋮ Transcendence and the Carlitz-Goss gamma function ⋮ All double coverings of cyclotomic fields ⋮ Periods of \(t\)-motives and transcendence ⋮ Special functions and Gauss-Thakur sums in higher rank and dimension ⋮ On the generalized Carlitz module ⋮ A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives ⋮ Frobenius difference equations and difference Galois groups ⋮ Zeta measure associated to \({\mathbb{F}}_ q[T\)] ⋮ Automata and transcendence in positive characteristic ⋮ Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields ⋮ Interpolation of hypergeometric ratios in a global field of positive characteristic ⋮ Deligne's reciprocity for function fields ⋮ Continued fraction for the exponential for \(\mathbb{F}_ q[T\)] ⋮ Product formulas for periods of CM abelian varieties and the function field analog ⋮ Double complex and gamma-monomials in global function fields ⋮ Integrable systems and number theory in finite characteristic ⋮ Anderson’s double complex and gamma monomials for rational function fields ⋮ Shtukas and Jacobi sums ⋮ Unnamed Item ⋮ Tensor powers of rank 1 Drinfeld modules and periods ⋮ Gauss sums for function fields ⋮ Linear independence of digamma function and a variant of a conjecture of Rohrlich ⋮ Special \(L\)-values and shtuka functions for Drinfeld modules on elliptic curves ⋮ \(\mathbb{F}_q\)-linear calculus over function fields ⋮ An alternate approach to solitons for \(\mathbb F_q [t\)] ⋮ Kronecker-Weber plus epsilon.

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