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arXiv · 2010.02025

$q$-Supercongruences with parameters

Chuanan Wei
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Abstract

In terms of the creative microscoping method recently introduced by Guo and Zudilin [Adv. Math. 346 (2019), 329--358], we find a $q$-supercongruence with four parameters modulo $Φ_n(q)(1-aq^n)(a-q^n)$, where $Φ_n(q)$ denotes the $n$-th cyclotomic polynomial in $q$. Then we empoly it and the Chinese remainder theorem for coprime polynomials to derive a $q$-supercongruence with two parameters modulo $[n]Φ_n(q)^3$, where $[n]=(1-q^n)/(1-q)$ is the $q$-integer.

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Chuanan Wei. 2020-10-02. $q$-Supercongruences with parameters. https://arxiv.org/abs/2010.02025

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