q-Analogues of Two Supercongruences of Z.-W. Sun

被引：15
|
作者：
Gu, Cheng-Yang [1 ]
Guo, Victor J. W. [1 ]
机构：
[1] Huaiyin Normal Univ, Sch Math & Stat, Huaian 223300, Jiangsu, Peoples R China
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2020年 / 70卷 / 03期
基金：
中国国家自然科学基金;
关键词：
congruences; q-binomial coefficient; cyclotomic polynomial; Franklin's involution; FINITE GENERALIZATIONS; NUMBERS;
D O I：
10.21136/CMJ.2020.0516-18
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give several different q-analogues of the following two congruences of Z.-W. Sun: Sigma(prX-1)/2 k=0 1 8k 2k k ! 2 pr (mod p2) and (prX-1)/2 k=0 116k 2k k ! 3 pr (mod p2), where p is an odd prime, r is a positive integer, and ( mn) is the Jacobi symbol. The proofs of them require the use of some curious q-series identities, two of which are related to Franklin's involution on partitions into distinct parts. We also confirm a conjecture of the latter author and Zeng in 2012.
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页码：757 / 765
页数：9
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