Some hypergeometric functions in positive characteristic and transcendence

Mao-Sheng Li

doi:10.1016/j.crma.2019.03.006

Number theory

Some hypergeometric functions in positive characteristic and transcendence

Presented by: the Editorial Board

Mao-Sheng Li ¹

¹ Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China

Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 317-322.

Abstract
Résumé

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.

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.

Received: 2019-01-26
Accepted: 2019-03-26
Published online: 2019-04-01

DOI: 10.1016/j.crma.2019.03.006

Author's affiliations:

Mao-Sheng Li ¹

¹ Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China

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     author = {Mao-Sheng Li},
     title = {Some hypergeometric functions in positive characteristic and transcendence},
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     pages = {317--322},
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     language = {en},
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Mao-Sheng Li. Some hypergeometric functions in positive characteristic and transcendence. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 317-322. doi : 10.1016/j.crma.2019.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.03.006/

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