A FAMILY OF q-SUPERCONGRUENCES MODULO THE CUBE OF A CYCLOTOMIC POLYNOMIAL

被引：21

作者：

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

Schlosser, Michael J. ^{[2
]}

机构：

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

[2] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2022年 / 105卷 / 02期

基金：

奥地利科学基金会; 中国国家自然科学基金;

关键词：

basic hypergeometric series; supercongruences; q-congruences; cyclotomic polynomial; Gasper's summation;

D O I：

10.1017/S0004972721000630

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish a family of q-supercongruences modulo the cube of a cyclotomic polynomial for truncated basic hypergeometric series. This confirms a weaker form of a conjecture of the present authors. Our proof employs a very-well-poised Karlsson-Minton type summation due to Gasper, together with the 'creative microscoping' method introduced by the first author in recent joint work with Zudilin.

引用

页码：296 / 302

页数：7

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