$q$-Supercongruences from squares of basic hypergeometric series
Number Theory
2021-12-23 v1
Abstract
We give some new -supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The main ingredients of our proofs are the creative microscoping method, a lemma of El Bachraoui, and the Chinese remainder theorem for coprime polynomials. We also propose several related conjectures for further study.
Cite
@article{arxiv.2112.12076,
title = {$q$-Supercongruences from squares of basic hypergeometric series},
author = {Victor J. W. Guo and Long Li},
journal= {arXiv preprint arXiv:2112.12076},
year = {2021}
}