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arXiv · 2001.08079

A family of $q$-congruences modulo the square of a cyclotomic polynomial

Victor J. W. Guo
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Abstract

Using Watson's terminating $_8\phi_7$ transformation formula, we prove a family of $q$-congruences modulo the square of a cyclotomic polynomial, which were originally conjectured by the author and Zudilin [J. Math. Anal. Appl. 475 (2019), 1636--646]. As an application, we deduce two supercongruences modulo $p^4$ ($p$ is an odd prime) and their $q$-analogues. This also partially confirms a special case of Swisher's (H.3) conjecture.

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Victor J. W. Guo. 2020-01-19. A family of $q$-congruences modulo the square of a cyclotomic polynomial. https://arxiv.org/abs/2001.08079

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