Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial

被引：4

作者：

Guo, Victor J. W. ^{[1
]}

机构：

[1] Huaiyin Normal Univ, Sch Math & Stat, Huaian 223300, Jiangsu, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2021年 / 76卷 / 02期

基金：

中国国家自然科学基金;

关键词：

cyclotomic polynomial; q-congruence; supercongruence; Swisher's conjecture; Bailey's transformation; Q-SUPERCONGRUENCES; SUMS; CONJECTURES;

D O I：

10.1007/s00025-021-01423-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using Bailey's (10)phi(9) transformation formula, we prove a family of q-congruences modulo the square of a cyclotomic polynomial, which were previously observed by the author and Zudilin (J Math Anal Appl 475:1636-1646, 2019). As an application, we confirm a conjecture in (Electron Res Arch 28:1031-1036, 2020). This also partially reproves a special case of Swisher's (H.3) conjecture.

引用

页数：12

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[1] Another Family of q-Congruences Modulo the Square of a Cyclotomic Polynomial
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[J]. Results in Mathematics, 2021, 76
[2] A FAMILY OF q-CONGRUENCES MODULO THE SQUARE OF A CYCLOTOMIC POLYNOMIAL
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[J]. ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (02): : 1031 - 1036
[3] Some symmetric q-congruences modulo the square of a cyclotomic polynomial
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[J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021, 115
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