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arXiv · 1104.3047

Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$

Zhi-Hong Sun
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Abstract

Let $p>3$ be a prime, and let $m$ be an integer with $p\nmid m$. In the paper, by using the work of Ishii and Deuring's theorem for elliptic curves with complex multiplication we solve some conjectures of Zhi-Wei Sun concerning $\sum_{k=0}^{p-1}\binom{2k}k^2\binom{4k}{2k}m^{-k}\mod {p^2}$.

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BibTeXRIS

Zhi-Hong Sun. 2011-04-15. Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$. https://arxiv.org/abs/1104.3047

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