Certain character sums and hypergeometric series
Number Theory
2018-02-14 v1
Abstract
We prove two transformations for the -adic hypergeometric series which can be described as -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 -adic hypergeometric series to deduce the transformations. We also find another transformation for the -adic hypergeometric series from which many special values of the -adic hypergeometric series as well as finite field hypergeometric functions are obtained.
Cite
@article{arxiv.1802.04503,
title = {Certain character sums and hypergeometric series},
author = {Rupam Barman and Neelam Saikia},
journal= {arXiv preprint arXiv:1802.04503},
year = {2018}
}
Comments
Pacific Journal of Mathematics (In press)