A $q$-supercongruence modulo the fourth power of a cyclotomic polynomial
Number Theory
2022-06-28 v2
Abstract
In this paper, a new -supercongruence with two free parameters modulo the fourth power of a cyclotomic polynomial is obtained. Our main auxiliary tools are Watson's transformation formula for basic hypergeometric series, the `creative microscoping' method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials. By taking suitable parameter substitutions in the established -supercongruence, some nice congruences involving the Bernoulli numbers are derived.
Keywords
Cite
@article{arxiv.2201.05785,
title = {A $q$-supercongruence modulo the fourth power of a cyclotomic polynomial},
author = {Xiaoxia Wang and Chang Xu},
journal= {arXiv preprint arXiv:2201.05785},
year = {2022}
}