Certain character sums and hypergeometric series

2018/02/13 by Barman, Rupam, Saikia, Neelam
#11S80 #11T24 #33C99 #33E50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.04503

Abstract

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.

Related

• Certain transformations and values of p-adic hypergeometric functions
• Zeros of p-adic hypergeometric functions, p-adic analogues of Kummer's and Pfaff's identities
• Certain Transformations for Hypergeometric series in p-adic setting
• Summation identities and transformations for hypergeometric series
• P-adic hypergeometrics