Supercongruences involving $p$-adic Gamma functions
Number Theory
2018-03-20 v6 Combinatorics
Abstract
We establish some supercongruences for the truncated and hypergeometric series involving the -adic Gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated hypergeometric series. The corresponding conjectural supercongruences modulo are also proposed for further research.
Cite
@article{arxiv.1611.07686,
title = {Supercongruences involving $p$-adic Gamma functions},
author = {Ji-Cai Liu},
journal= {arXiv preprint arXiv:1611.07686},
year = {2018}
}
Comments
to appear in Bulletin of the Australian Mathematical Society, 11 pages