A family of q-hypergeometric congruences modulo
the fourth power of a cyclotomic polynomial
(12 pages)
Abstract
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.
The following version is available:
Back to Michael Schlosser's
home page.