Some 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 : 2021-01-01 Epub Date: 2021-05-31 DOI:10.1007/s13398-021-01070-y

Victor J W Guo, Michael J Schlosser

引用次数: 5

Abstract

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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对一个环形多项式的平方和立方取模的一些q-超同余。

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。

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

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