Comptes Rendus
Number Theory
Hypergeometric functions for function fields and transcendence
[Fonctions hypergéométriques pour les corps de fonctions et transcendance]
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 q1 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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