English

Certain character sums and hypergeometric series

Number Theory 2018-02-14 v1

Abstract

We prove two transformations for the pp-adic hypergeometric series which can be described as pp-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 pp-adic hypergeometric series to deduce the transformations. We also find another transformation for the pp-adic hypergeometric series from which many special values of the pp-adic hypergeometric series as well as finite field hypergeometric functions are obtained.

Keywords

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)

R2 v1 2026-06-23T00:20:32.252Z