Certain transformations and values of p-adic hypergeometric functions

2022/04/21 by Sulakashna, Barman, Rupam
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2204.10311

Abstract

We prove two transformations for the p-adic hypergeometric functions which can be described as p-adic analogues of a Euler's transformation and a transformation of Clausen. We first evaluate certain character sums, and then relate them to the p-adic hypergeometric functions to deduce the transformations. We use a character sum identity proved by Ahlgren, Ono, and Penniston to deduce the p-adic Clausen's transformation. We also deduce special values of certain p-adic hypergeometric functions.

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