Some new $q$-congruences for truncated basic hypergeometric series: even powers
Number Theory
2019-12-02 v2 Combinatorics
Abstract
We provide several new -congruences for truncated basic hypergeometric series with the base being an even power of . Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing -congruences for truncated basic hypergeometric series with the base being an odd power of . We also give a number of related conjectures including -congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.
Cite
@article{arxiv.1904.00490,
title = {Some new $q$-congruences for truncated basic hypergeometric series: even powers},
author = {Victor J. W. Guo and Michael J. Schlosser},
journal= {arXiv preprint arXiv:1904.00490},
year = {2019}
}
Comments
13 pages, more background and references added