Supercongruences for truncated hypergeometric series and p-adic gamma function
Number Theory
2018-07-11 v5
Abstract
We prove three more general supercongruences between truncated hypergeometric series and -adic Gamma function from which some known supercongruences follow. A supercongruence conjectured by Rodriguez-Villegas and proved by E. Mortenson using the theory of finite field hypergeometric series follows from one of our more general supercongruences. We also prove a supercongruence for truncated hypergeometric series which is similar to a supercongruence proved by L. Long and R. Ramakrishna.
Cite
@article{arxiv.1507.07391,
title = {Supercongruences for truncated hypergeometric series and p-adic gamma function},
author = {Rupam Barman and Neelam Saikia},
journal= {arXiv preprint arXiv:1507.07391},
year = {2018}
}
Comments
To appear in Mathematical Proceedings Cambridge Phil. Soc