Hypergeometric functions for function fields and transcendence

被引：3

作者：

Thakur, Dinesh S. ^{[2
]}

Wen, Zhi-Ying ^{[1
]}

Yao, Jia-Yan ^{[1
]}

Zhao, Liang ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

来源：

COMPTES RENDUS MATHEMATIQUE | 2009年 / 347卷 / 9-10期

基金：

中国国家自然科学基金;

关键词：

GOSS GAMMA FUNCTION; VALUES; CRITERION;

D O I：

10.1016/j.crma.2009.03.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study hypergeometric functions for F-q vertical bar T vertical bar, 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. To cite this article: D.S. Thakur et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：467 / 472

页数：6

共 21 条

[1] Transcendence of the Carlitz-Goss gamma function at rational arguments [J].

Allouche, JP .

JOURNAL OF NUMBER THEORY, 1996, 60 (02) :318-328

[2] Determination of the algebraic relations among special Γ-values in positive characteristic [J].

Anderson, GW ;

Brownawell, WD ;

Papanikolas, MA .

ANNALS OF MATHEMATICS, 2004, 160 (01) :237-313

[3] Transcendental values of Bessel-Carlitz functions [J].

Denis, L .

ARKIV FOR MATEMATIK, 1998, 36 (01) :73-85

[4] Criterion of transcendence in finite characteristic [J].

Denis, L .

JOURNAL OF ALGEBRA, 1996, 182 (02) :522-533

[5]

France MM, 1997, J NUMBER THEORY, V63, P396

[6] ALGEBRAIC ELEMENTS IN FORMAL POWER-SERIES RINGS [J].

HARASE, T .

ISRAEL JOURNAL OF MATHEMATICS, 1988, 63 (03) :281-288

[7] Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms [J].

Papanikolas, Matthew A. .

INVENTIONES MATHEMATICAE, 2008, 171 (01) :123-174

[8]

SHARIF H, 1988, J LOND MATH SOC, V37, P395

[9]

THAKUR D. S., 2000, J. Ramanujan Math. Soc., V15, P43

[10]

THAKUR D. S., 1995, Finite Fields Appl., V1, P219

← 1 2 3 →