A further $q$-generalization of the (C.2) and (G.2) supercongruences of Van Hamme

Song-Xiao Li; Su-Dan Wang

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arXiv · 2603.26223

A further $q$-generalization of the (C.2) and (G.2) supercongruences of Van Hamme

Song-Xiao Li·Su-Dan Wang

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Abstract

Applying the $q$-Zeilberger algorithm, we establish a unified $q$-analogue of the (C.2) and (G.2) supercongruences of Van Hamme, which can be viewed as a refinement of several previously known results. As consequences, we obtain a $q$-analogue of supercongruence involving Bernoulli numbers, as well as a refinement of (G.2) supercongruence.

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Song-Xiao Li, Su-Dan Wang. 2026-03-27. A further $q$-generalization of the (C.2) and (G.2) supercongruences of Van Hamme. https://arxiv.org/abs/2603.26223

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