Number Theory
Special values of fractional hypergeometric functions for function fields
Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 801-806.

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.

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.

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DOI: 10.1016/j.crma.2012.10.002
Yao, Jia-Yan 1

1 Department of Mathematics, Tsinghua University, Beijing 100084, PR China
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Yao, Jia-Yan. 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. http://www.numdam.org/articles/10.1016/j.crma.2012.10.002/

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