Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial

被引：4
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：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2023年 / 117卷 / 01期
基金：
奥地利科学基金会;
关键词：
Basic hypergeometric series; Supercongruences; q-congruences; Cyclotomic polynomial; Gasper's summation;
D O I：
10.1007/s13398-022-01338-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper, the method of creative microscoping (a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.
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页数：11
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