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arXiv · 2608.13818

Some Dwork-type $q$-supercongruences from a $_6\phi_5$ summation formula

Chuanan Wei·Qin Wang
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Abstract

With the help of a $_6\phi_5$ summation formula and Guo and Zudilin's method, we shall establish some Dwork-type $q$-supercongruences in this paper. When $q\to1$, these $q$-supercongruences are able to engender the corresponding supercongruences. One of them may be stated as follows: for any prime $p\geq5$ and any positive integer $s$, \begin{align*} &\sum_{k=0}^{p^s-1}(6k-1)\frac{(-\frac{1}{3})_k^3}{(1)_k^3} \equiv 0\pmod{p^{3s}}. \end{align*}

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Chuanan Wei, Qin Wang. 2026-08-13. Some Dwork-type $q$-supercongruences from a $_6\phi_5$ summation formula. https://arxiv.org/abs/2608.13818

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