Hypergeometric functions for function fields and transcendence

Dinesh S. Thakur; Zhi-Ying Wen; Jia-Yan Yao; Liang Zhao

doi:10.1016/j.crma.2009.03.006

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. 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

Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 467-472.

Résumé
Abstract

Nous étudions les fonctions hypergéométriques pour $F_{q} [T]$ , 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 $F_{q} [T]$ , 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 : 2008-12-23
Accepté le : 2009-03-02
Publié le : 2009-04-03

DOI : 10.1016/j.crma.2009.03.006

Affiliations des auteurs :

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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     title = {Hypergeometric functions for function fields and transcendence},
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     pages = {467--472},
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     doi = {10.1016/j.crma.2009.03.006},
     language = {en},
}

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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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