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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 Epub Date: 2022-10-16 DOI:10.1007/s13398-022-01338-x

Victor J W Guo, Michael J Schlosser

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.

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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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.