q-Analogues of two Ramanujan-type supercongruences

被引：26
|
作者：
Liu, Yudong [1 ]
Wang, Xiaoxia [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 502卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Basic hypergeometric series; Supercongruences; q-Congruences; q-Analogue; Cyclotomic polynomial; CONJECTURES;
D O I：
10.1016/j.jmaa.2021.125238
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish a new q-congruence with parameters modulo the fourth power of a cyclotomic polynomial from Watson's (8)phi(7) transformation. Taking parameters substitution in our new q-congruence, we present a q-analogue of the (D.2) supercongruenceof Van Hamme and several different q-analogues of He's supercongruence for p equivalent to 1(mod3). Finally, we propose a Dwork-type supercongruence conjecture on He's supercongruence. (C) 2021 Elsevier Inc. All rights reserved.
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页数：14
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