Some $q$-supercongruences modulo the square and cube of a cyclotomic polynomial
Number Theory
2021-01-26 v1
Abstract
Two -supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two -supercongruences that were earlier conjectured by the same authors and involve -supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved -supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.
Keywords
Cite
@article{arxiv.2101.09753,
title = {Some $q$-supercongruences modulo the square and cube of a cyclotomic polynomial},
author = {Victor J. W. Guo and Michael J. Schlosser},
journal= {arXiv preprint arXiv:2101.09753},
year = {2021}
}
Comments
10 pages