English

Supercongruences involving $p$-adic Gamma functions

Number Theory 2018-03-20 v6 Combinatorics

Abstract

We establish some supercongruences for the truncated 2F1{}_2F_1 and 3F2{}_3F_2 hypergeometric series involving the pp-adic Gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated 3F2{}_3F_2 hypergeometric series. The corresponding conjectural supercongruences modulo p3p^3 are also proposed for further research.

Keywords

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

R2 v1 2026-06-22T17:01:56.895Z