A family of $q$-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial

Victor J. W. Guo, Michael J. Schlosser

Published 2019-09-23Version 1

We prove a two-parameter family of $q$-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial. Crucial ingredients in our proof are George Andrews' multiseries extension of the Watson transformation, and a Karlsson--Minton type summation for very-well-poised basic hypergeometric series due to George Gasper. The new family of $q$-congruences is then used to prove two conjectures posed earlier by the authors.