Explicit families of congruences for the overpartition function

TL;DR

This paper presents new explicit families of congruences for the overpartition function, extending previous theoretical results to concrete infinite and finite families for various moduli.

Contribution

It provides explicit, effective families of congruences for the overpartition function for specific moduli, advancing the understanding of its arithmetic properties.

Findings

Infinite families of congruences modulo 5, 7, 11

Finite families of congruences modulo 13, 17, 19

Builds on and makes effective previous existence results by Treneer

Abstract

In this article we exhibit new explicit families of congruences for the overpartition function, making effective the existence results given previously by Treneer. We give infinite families of congruences modulo $m$ for $m = 5, 7, 11$, and finite families for $m = 13, 17, 19$.