English

$q$-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 qq-supercongruence for double series and a qq-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}
}