English

Some $q$-supercongruences modulo the square and cube of a cyclotomic polynomial

Number Theory 2021-01-26 v1

Abstract

Two qq-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 qq-supercongruences that were earlier conjectured by the same authors and involve qq-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved qq-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