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arXiv · 2110.10361

Some $q$-congruences involving central $q$-binomial coefficients

He-Xia Ni
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Abstract

Suppose that $p$ is an odd prime and $m$ is an integer not divisible by $p$. Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave $\sum_{k=0}^{n-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=0}^{n-1}\binom{2k}{k+d}/(km^k)$ modulo $p$ for all $d=0,1, \ldots n$ and $n= p^a$, where $a$ is a positive integer. In this paper, we present some $q$-analogues of these congruences in the cases $m=2, 4$ for any positive integer $n$.

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He-Xia Ni. 2021-10-20. Some $q$-congruences involving central $q$-binomial coefficients. https://arxiv.org/abs/2110.10361

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