Some q-supercongruences modulo the fourth power of a cyclotomic polynomial,Journal of Combinatorial Theory Series A

当前位置： X-MOL 学术 › J. Comb. Theory A › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Some q-supercongruences modulo the fourth power of a cyclotomic polynomial
Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2021-04-15 , DOI: 10.1016/j.jcta.2021.105469
Chuanan Wei

With the help of the creative microscoping method recently introduced by Guo and Zudilin and the Chinese remainder theorem for coprime polynomials, we establish a q-supercongruence with two parameters modulo $[n] Φ_{n} {(q)}^{3}$ . Here $[n] = (1 - q^{n}) / (1 - q)$ and $Φ_{n} (q)$ is the n-th cyclotomic polynomial in q. In particular, we confirm a recent conjecture of Guo and give a complete q-analogue of Long's supercongruence. The latter is also a generalization of a recent q-supercongruence obtained by Guo and Schlosser.

更新日期：2021-04-15

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文本刊介绍/投稿指南

全部期刊列表>>