($q$-)Supercongruences hit again

TL;DR

This paper develops a $q$-hypergeometric approach to generalize Dwork-type supercongruences involving hypergeometric sums related to Calabi--Yau threefolds, extending known congruences to higher powers of primes.

Contribution

It introduces an intrinsic $q$-hypergeometric method to generalize supercongruences for hypergeometric sums associated with Calabi--Yau threefolds.

Findings

Generalized Dwork-type supercongruences for hypergeometric sums

Established congruences modulo $p^3$ for primes $p$

Extended known supercongruences to higher prime powers

Abstract

Using an intrinsic $q$-hypergeometric strategy, we generalise Dwork-type congruences $H(p^{s+1})/H(p^s)\equiv H(p^s)/H(p^{s-1})\pmod{p^3}$ for $s=1,2,\dots$ and $p$ a prime, when $H(N)$ are truncated hypergeometric sums corresponding to the periods of rigid Calabi--Yau threefolds.