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.
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页码：296 / 302
页数：7
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