两个奇特的 q 超共轭及其扩展

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-01-01 DOI:10.1515/forum-2023-0164

Haihong He, Xiaoxia Wang

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引用次数: 0

摘要

我们证明了郭明錤最近猜想的两个单参数 q-supercongruences ，并在多一个参数的情况下建立了它们的进一步扩展。证明的关键要素是 q 二项式定理的终结形式、Gasper 提出的卡尔松-明顿式求和公式，以及郭和祖迪林提出的 "创造性微观 "方法。顺便提一下，李、唐和王的一个论断也通过建立其 q-analogue 得到了证实。

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Two curious q-supercongruences and their extensions

We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of the q-binomial theorem, a Karlsson–Minton-type summation formula due to Gasper, and the method of “creative microscoping” developed by Guo and Zudilin. Incidentally, an assertion of Li, Tang and Wang is also confirmed by establishing its q-analogue.

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.