$p$-adic analogues of hypergeometric identities and their applications

Chen Wang; Zhi-Wei Sun

paper

$p$ -adic analogues of hypergeometric identities and their applications

arXiv:1910.06856

Abstract

In this paper, we confirm several conjectures posed by Sun recently; for example, we prove that for any odd prime $p$ we have $k = 0 \sum p - 1 A_{k} \equiv {4 x^{2} - 2 p (mod p^{2}) 0 (mod p^{2}) if p = x^{2} + 2 y^{2} (x, y \in Z), if p \equiv 5, 7 (mod 8),$ where $A_{n} := \sum_{k = 0}^{n} (k n + k)^{2} (k n)^{2}$ are the Apéry numbers.

19 pages

References in corpus (1)

Proof of a congruence concerning truncated hypergeometric series $_{6} F_{5}$

p-adic analogues of hypergeometric identities and their applications

Abstract

References in corpus (1)

$p$ -adic analogues of hypergeometric identities and their applications