CERTAIN CHARACTER SUMS AND HYPERGEOMETRIC SERIES

被引：5

作者：

Barman, Rupam ^{[1
]}

Saikia, Neelam ^{[1
]}

机构：

[1] Indian Inst Technol Guwahati, Dept Math, Gauhati, Assam, India

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2018年 / 295卷 / 02期

关键词：

character sum; hypergeometric series; p-adic gamma function; ELLIPTIC-CURVES; SPECIAL VALUES; FINITE-FIELDS; FROBENIUS; TRACE;

D O I：

10.2140/pjm.2018.295.271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove two transformations for the p-adic hypergeometric series which can be described as p-adic analogues of a Kummer's linear transformation and a transformation of Clausen. We first evaluate two character sums, and then relate them to the p-adic hypergeometric series to deduce the transformations. We also find another transformation for the p-adic hypergeometric series from which many special values of the p-adic hypergeometric series as well as finite field hypergeometric functions are obtained.

引用

页码：271 / 289

页数：19

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