Ramanujan-type supercongruences

TL;DR

This paper introduces new supercongruences as p-adic analogues of Ramanujan series for 1/π and 1/π^2, and provides proofs for three specific cases.

Contribution

It presents novel p-adic supercongruences related to Ramanujan-type series and proves three of these conjectured identities.

Findings

Three supercongruences proved as p-adic analogues of Ramanujan series.

New connections established between supercongruences and Ramanujan-type series.

Enhanced understanding of p-adic properties of series related to 1/π and 1/π^2.

Abstract

We present several supercongruences that may be viewed as $p$-adic analogues of Ramanujan-type series for $1/\pi$ and $1/\pi^2$, and prove three of these examples.