$q$-Supercongruences for multidimensional series modulo the sixth power of a cyclotomic polynomial
Combinatorics
2024-08-06 v1 Number Theory
Abstract
With the help of El Bachraoui's lemma, the creative microscoping method, and a new form of the Chinese remainder theorem for coprime polynomials, we prove a -supercongruence for double series and a -supercongruence for triple series modulo the sixth power of a cyclotomic polynomial. As conclusions, two corresponding supercongruences for double and triple series, which are associated with the (D.2) supercongruence of Van Hamme, are given.
Keywords
Cite
@article{arxiv.2408.02002,
title = {$q$-Supercongruences for multidimensional series modulo the sixth power of a cyclotomic polynomial},
author = {Chuanan Wei},
journal= {arXiv preprint arXiv:2408.02002},
year = {2024}
}