[Valeurs spéciales des fonctions hypergéométriques fractionnaires pour les corps de fonctions]
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.
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@article{CRMATH_2012__350_17-18_801_0,
author = {Yao, Jia-Yan},
title = {Special values of fractional hypergeometric functions for function fields},
journal = {Comptes Rendus. Math\'ematique},
pages = {801--806},
publisher = {Elsevier},
volume = {350},
number = {17-18},
year = {2012},
doi = {10.1016/j.crma.2012.10.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.10.002/}
}
TY - JOUR AU - Yao, Jia-Yan TI - Special values of fractional hypergeometric functions for function fields JO - Comptes Rendus. Mathématique PY - 2012 SP - 801 EP - 806 VL - 350 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.10.002/ DO - 10.1016/j.crma.2012.10.002 LA - en ID - CRMATH_2012__350_17-18_801_0 ER -
%0 Journal Article %A Yao, Jia-Yan %T Special values of fractional hypergeometric functions for function fields %J Comptes Rendus. Mathématique %D 2012 %P 801-806 %V 350 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.10.002/ %R 10.1016/j.crma.2012.10.002 %G en %F CRMATH_2012__350_17-18_801_0
Yao, Jia-Yan. Special values of fractional hypergeometric functions for function fields. Comptes Rendus. Mathématique, Tome 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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