Special values of fractional hypergeometric functions for function fields

Jia-Yan Yao

doi:10.1016/j.crma.2012.10.002

Number Theory

Special values of fractional hypergeometric functions for function fields
[Valeurs spéciales des fonctions hypergéométriques fractionnaires pour les corps de fonctions]

Présenté par : the Editorial Board

Jia-Yan Yao ¹

¹ Department of Mathematics, Tsinghua University, Beijing 100084, PR China

Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 801-806.

Résumé
Abstract

Dans ce travail nous étudions les fonctions hypergéométriques fractionnaires pour les corps de fonctions, introduites par D.S. Thakur. Nous caractérisons celles de ces fonctions qui sont algébriques, et nous démontrons la transcendance de valeurs spéciales en certains arguments algébriques non nuls de celles qui sont des fonctions transcendantes entières.

In this work we study the fractional hypergeometric functions for function fields, introduced by D.S. Thakur. We shall characterize algebraic functions among them, and show the transcendence of special values at some nonzero algebraic arguments, in the case when they are entire transcendental functions.

Reçu le : 2012-08-30
Accepté le : 2012-10-02
Publié le : 2012-09-01

DOI : 10.1016/j.crma.2012.10.002

Affiliations des auteurs :

Jia-Yan Yao ¹

¹ Department of Mathematics, Tsinghua University, Beijing 100084, PR China

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Jia-Yan Yao. Special values of fractional hypergeometric functions for function fields. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 801-806. doi : 10.1016/j.crma.2012.10.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.002/

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