Special values of fractional hypergeometric functions for function fields
type: Item
instance of: scholarly article
title: Special values of fractional hypergeometric functions for function fields
zbMATH Open document ID: 1264.11066
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2012-11-22T00:00:00Z
review text: Hypergeometric functions over a function field were introduced by \textit{D. S. Thakur} [Finite Fields Appl. 1, No. 2, 219--231 (1995; Zbl 0838.11043)]; see also the reviewer's ``Analysis in positive characteristic.'' Cambridge: Cambridge University Press (2009; Zbl 1171.12005)]. The author characterizes algebraic functions within the above class, and shows the transcendence of special values at some nonzero algebraic arguments. For related results see also [\textit{D. S. Thakur, Z.-Y. Wen}, the author and \textit{L. Zhao}, J. Reine Angew. Math. 657, 135--171 (2011; Zbl 1227.11088)].
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 11J91
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 33E50
zbMATH DE Number: 6109859
zbMATH Keywords: hypergeometric function
zbMATH Keywords: function field
author: Jia-Yan Yao
MaRDI profile type: Publication
full work available at URL: j.crma.2012.10.002
OpenAlex ID: W2032486640
cites work: Q1811520
cites work: Monodromy for the hypergeometric function \(_ nF_{n-1}\)
cites work: \(p\)-adic cycles
cites work: Q5622359
cites work: Evolution equations and functions of hypergeometric type over fields of positive characteristics
cites work: Hypergeometric Functions and Carlitz Differential Equations over Function Fields
cites work: Q3615516
cites work: Hypergeometric functions for function fields
cites work: Q4488714
cites work: Q3158374
cites work: Hypergeometric functions for function fields and transcendence
cites work: Transcendence in positive characteristic and special values of hypergeometric functions
cites work: Two types of function field transcendental numbers
cites work: Q4223129
cites work: Some transcendental functions over function fields with positive characteristic.
DOI: 10.1016/J.CRMA.2012.10.002
description: scientific article; zbMATH DE number 6109859