对一个环形多项式的平方和立方取模的一些q-超同余。

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 Epub Date: 2021-05-31 DOI:10.1007/s13398-021-01070-y

Victor J W Guo, Michael J Schlosser

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引用次数: 5

摘要

利用基本超几何级数的特殊恒等式，建立了包含两个自由参数的截断的基本超几何级数的两个q-超同余。结果部分地推广了先前由同一作者推测的两个q-超同余，并且涉及到q-超同余模取一个环多项式的平方和立方。其中一个新证明的q-超同余甚至被推测为对分环多项式的四次幂取模。

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

Two q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved q-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.

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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.