Supercongruences involving $p$-adic Gamma functions

Abstract

We establish some supercongruences for the truncated ${}_2{F}_1$ and ${}_3{F}_2$ hypergeometric series involving the $p$-adic Gamma functions. Some of these results extend the four Rodriguez-Villegas supercongruences on the truncated ${}_3{F}_2$ hypergeometric series. The corresponding conjectural supercongruences modulo $p^3$ are also proposed for further research.

to appear in Bulletin of the Australian Mathematical Society, 11 pages

References in corpus (1)

• An elementary proof of a Rodriguez-Villegas supercongruence

Cited by in corpus (2)

• Supercongruences related to ${}_3{F}_2(1)$ involving harmonic numbers
• Supercongruences between truncated ${}_3{F}_2$ hypergeometric series