Victor J. W. Guo
Published 2020-01-19Version 1
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.
$q$-Supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping
Some $q$-supercongruences modulo the square and cube of a cyclotomic polynomial
Two new $q$-supercongruences arising from Carlitz's identity
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