Certain transformations and values of p-adic hypergeometric functions
Number Theory
2022-04-22 v1
Abstract
We prove two transformations for the -adic hypergeometric functions which can be described as -adic analogues of a Euler's transformation and a transformation of Clausen. We first evaluate certain character sums, and then relate them to the -adic hypergeometric functions to deduce the transformations. We use a character sum identity proved by Ahlgren, Ono, and Penniston to deduce the -adic Clausen's transformation. We also deduce special values of certain -adic hypergeometric functions.
Cite
@article{arxiv.2204.10311,
title = {Certain transformations and values of p-adic hypergeometric functions},
author = {Sulakashna and Rupam Barman},
journal= {arXiv preprint arXiv:2204.10311},
year = {2022}
}
Comments
13 pages. arXiv admin note: text overlap with arXiv:1802.04503