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

By Victor J. W. Guo, Michael J. Schlosser. Israel Journal of Mathematics, 2019

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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.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

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