Proof of Some q-Supercongruences Modulo the Fourth Power of a Cyclotomic Polynomial

Abstract

We prove some q-supercongruences modulo the fourth power of a cyclotomic polynomial by making use of the Chinese remainder theorem for coprime polynomials, Watson’s $$_8\phi _7$$ transformation, and the ‘creative microscoping’ method introduced by the author and Wadim Zudilin. In particular, we confirm Conjecture 1.5 in (Results Math 74:131, 2019).