$p$-adic analogues of hypergeometric identities

Abstract

We prove some supercongruences for the truncated hypergeometric series.

This is a preliminary draft, which maybe contains some mistakes. Several new congruences have been added in the second version

References in corpus (3)

• Supercongruences for rigid hypergeometric Calabi--Yau threefolds
• A modular supercongruence for ${}_6{F}_5$: an Apéry-like story
• Supercongruences related to ${}_3{F}_2(1)$ involving harmonic numbers

Cited by in corpus (8)

• Supercongruences concerning truncated hypergeometric series
• Proof of a conjecture of Adamchuk
• On two conjectural supercongruences of Z.-W. Sun
• On the divisibility of some truncated hypergeometric series
• $p$-adic analogues of hypergeometric identities and their applications
• A parametric congruence motivated by Orr's identity
• Some Numeric Hypergeometric Supercongruences
• Three pairs of congruences concerning sums of central binomial coefficients