Comptes Rendus
no. 9-10
Number Theory
Hypergeometric functions for function fields and transcendence
[Fonctions hypergéométriques pour les corps de fonctions et transcendance]

Présenté par : Jean-Pierre Kahane

Dinesh S. Thakur1 ; Zhi-Ying Wen2 ; Jia-Yan Yao2  ; Liang Zhao2
1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
2 Department of Mathematics, Tsinghua University, Beijing 100084, PR China
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 467-472.

Nous étudions les fonctions hypergéométriques pour Fq[T], et démontrons dans le cas entier (non polynomial) la transcendance de leurs valeurs spéciales aux arguments algébriques non nuls qui engendrent des extensions du corps de fonctions rationnelles avec au plus q−1 places à l'infini. Nous caractérisons aussi dans le cas équilibré l'algébricité des fonctions hypergéométriques.

We study hypergeometric functions for Fq[T], and show in the entire (non-polynomial) case the transcendence of their special values at nonzero algebraic arguments which generate extension of the rational function field with less than q places at infinity. We also characterize in the balanced case the algebraicity of hypergeometric functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.03.006
Dinesh S. Thakur 1 ; Zhi-Ying Wen 2 ; Jia-Yan Yao 2 ; Liang Zhao 2

1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA
2 Department of Mathematics, Tsinghua University, Beijing 100084, PR China 
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Dinesh S. Thakur; Zhi-Ying Wen; Jia-Yan Yao; Liang Zhao. Hypergeometric functions for function fields and transcendence. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 467-472. doi : 10.1016/j.crma.2009.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.006/

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