no. 4
Number theory
Some hypergeometric functions in positive characteristic and transcendence
[Quelques fonctions hypergéométriques en caractéristique positive et transcendance]

Présenté par : the Editorial Board

Li, Mao-Sheng1
1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China
Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 317-322.

Nous étudions dans ce travail certaines fonctions hypergéométriques spéciales en caractéristique positive, introduites par D. S. Thakur. Nous allons établir des relations fonctionnelles auxquelles elles satisfont, et déduire, à l'aide de la version pour les corps de fonctions du théorème de Schneider–Lang obtenue par J. Yu, qu'au moins l'une de leurs valeurs aux arguments algébriques non nuls est transcendante.

In this work, we study some special hypergeometric functions in positive characteristic, introduced by D. S. Thakur. We shall establish functional relationships among them, and deduce, with the help of the function field version of the Schneider–Lang theorem obtained by J. Yu, that at least one of their values at nonzero algebraic arguments is transcendental.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.03.006
Li, Mao-Sheng 1

1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China 
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Li, Mao-Sheng. Some hypergeometric functions in positive characteristic and transcendence. Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 317-322. doi : 10.1016/j.crma.2019.03.006. http://www.numdam.org/articles/10.1016/j.crma.2019.03.006/

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