Summation identities and transformations for hypergeometric series

被引：4
作者：
Barman R. [1 ]
Saikia N. [1 ]
机构：
[1] Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati
来源：
Annales mathématiques du Québec | 2018年 / 42卷 / 2期
关键词：
Algebraic curves; Character of finite fields; Gauss sums; Gaussian hypergeometric series; Jacobi sums; p-adic Gamma function; p-adic hypergeometric series; Teichmüller character;
D O I：
10.1007/s40316-017-0087-9
中图分类号：
学科分类号：
摘要：
We find summation identities and transformations for the McCarthy’s p-adic hypergeometric series by evaluating certain Gauss sums which appear while counting points on the family Zλ:x1d+x2d=dλx1x2d-1over a finite field Fp. Salerno expresses the number of points over a finite field Fp on the family Zλ in terms of quotients of p-adic gamma functions under the condition that d| p- 1. In this paper, we first express the number of points over a finite field Fp on the family Zλ in terms of McCarthy’s p-adic hypergeometric series for any odd prime p not dividing d(d- 1) , and then deduce two summation identities for the p-adic hypergeometric series. We also find certain transformations and special values of the p-adic hypergeometric series. We finally find a summation identity for the Greene’s finite field hypergeometric series. © 2017, Fondation Carl-Herz and Springer International Publishing AG.
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页码：133 / 157
页数：24
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