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

IF 1.8 2区 数学 Q1 MATHEMATICS
Victor J W Guo, Michael J Schlosser
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引用次数: 4

Abstract

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.

三个q-超共轭族模分圆多项式的平方和立方体。
本文证明了截断的非常匀称的基本超几何级数的三个参数q-超同余,其中一个是模一个环多项式的平方,另外两个是模一个环多项式的立方。证明的主要成分包括乔治·加斯珀(George Gasper)的一个基本的超几何求和,创造性显微镜法(最近由第一作者与瓦迪姆·祖迪林(Wadim Zudilin)合作引入的一种方法),以及质数多项式的中国剩余定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.70
自引率
17.20%
发文量
151
审稿时长
>12 weeks
期刊介绍: The journal publishes, in English language only, high-quality Research Articles covering Algebra; Applied Mathematics; Computational Sciences; Geometry and Topology; Mathematical Analysis; Statistics and Operations Research. Also featured are Survey Articles in every mathematical field.
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