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

Zhi-Hong Sun

paper

Congruences involving $(k 2 k)^{2} (2 k 4 k) m^{- k}$

arXiv:1104.3047

Abstract

Let $p > 3$ be a prime, and let $m$ be an integer with $p ∤ m$ . 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 $\sum_{k = 0}^{p - 1} (k 2 k)^{2} (2 k 4 k) m^{- k} mod p^{2}$ .

14 pages

References in corpus (1)

Point counting on reductions of CM elliptic curves

Congruences involving (k2k​)2(2k4k​)m−k

Abstract

References in corpus (1)

Congruences involving $(k 2 k)^{2} (2 k 4 k) m^{- k}$