q-Analogues of the (E.2) and (F.2) supercongruences of Van Hamme

被引：33
作者：
Guo, Victor J. W. [1 ]
机构：
[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China
来源：
RAMANUJAN JOURNAL | 2019年 / 49卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Ramanujan; Supercongruences; q-Analogues; Cyclotomic polynomials; q-WZ pair; CONGRUENCES;
D O I：
10.1007/s11139-018-0021-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Motivated by Zudilin's work, we give q-analogues of the Ramanujan-type supercongruences (E.2) and (F.2) of Van Hamme. Our proof utilizes the q-WZ method and properties of cyclotomic polynomials. Using the same q-WZ pair, we also give q-analogues of some similar supercongruences due to He and Swisher. Additionally, we propose several related conjectures on supercongruences or q-supercongruences.
引用
收藏
页码：531 / 544
页数：14
相关论文
共 20 条
[1]   q-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher [J].
Andrews, GE .
DISCRETE MATHEMATICS, 1999, 204 (1-3) :15-25
[2]  
[Anonymous], 2004, ENCY MATH ITS APPL
[3]   Generators of some Ramanujan formulas [J].
Guillera, J .
RAMANUJAN JOURNAL, 2006, 11 (01) :41-48
[4]   A q-analogue of a Ramanujan-type supercongruence involving central binomial coefficients [J].
Guo, Victor J. W. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 458 (01) :590-600
[5]   The Rodriguez-Villegas type congruences for truncated q-hypergeometric functions [J].
Guo, Victor J. W. ;
Pan, Hao ;
Zhang, Yong .
JOURNAL OF NUMBER THEORY, 2017, 174 :358-368
[6]   Some q-supercongruences for truncated basic hypergeometric series [J].
Guo, Victor J. W. ;
Zeng, Jiang .
ACTA ARITHMETICA, 2015, 171 (04) :309-326
[7]   Some q-analogues of supercongruences of Rodriguez-Villegas [J].
Guo, Victor J. W. ;
Zeng, Jiang .
JOURNAL OF NUMBER THEORY, 2014, 145 :301-316
[8]   Some congruences involving central q-binomial coefficients [J].
Guo, Victor J. W. ;
Zeng, Jiang .
ADVANCES IN APPLIED MATHEMATICS, 2010, 45 (03) :303-316
[9]   SOME CONGRUENCES ON TRUNCATED HYPERGEOMETRIC SERIES [J].
He, Bing .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (12) :5173-5180
[10]   A generalization of Morley's congruence [J].
Liu, Jianxin ;
Pan, Hao ;
Zhang, Yong .
ADVANCES IN DIFFERENCE EQUATIONS, 2015,
12