Two curious q-supercongruences and their extensions

被引：9
作者：
He, Haihong [1 ,2 ]
Wang, Xiaoxia [1 ,2 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China
来源：
FORUM MATHEMATICUM | 2024年 / 36卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Congruence; cyclotomic polynomial; Karlsson-Minton-type summation; creative microscoping;
D O I：
10.1515/forum-2023-0164
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the q-binomial theorem, a Karlsson-Minton-type summation formula due to Gasper, and the method of "creative microscoping" developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang and Wang is also confirmed by establishing its q-analogue.
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页码：1555 / 1563
页数：9
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