On $p$-adic expansions of Ramanujan-like series

TL;DR

This paper explores conjectured $p$-adic expansions related to Ramanujan-like series for powers of $1/\pi$, inspired by supercongruences patterns, aiming to deepen understanding of their arithmetic properties.

Contribution

It introduces new conjectures on $p$-adic expansions for Ramanujan-like series, extending the supercongruences pattern to a broader context.

Findings

Proposes conjectural $p$-adic expansion formulas

Links supercongruences to $p$-adic properties of Ramanujan series

Provides evidence and motivation for future proofs

Abstract

Inspired by a Zudilin-Zhao's supercongruences pattern related to Ramanujan-like series for $1/\pi^k$, we conjecture a kind of $p$-adic expansions.