New congruences for $\ell$-regular overpartitions

TL;DR

This paper presents new congruences modulo 5 for the $ ell$-regular overpartition function when $ ell$ is a power of 5, extending the understanding of its arithmetic properties.

Contribution

It introduces novel congruences for the $ ell$-regular overpartition function specifically for powers of 5, building on prior research.

Findings

New congruences modulo 5 for $ ell$-regular overpartitions

Results apply when $ ell$ is a power of 5

Enhances understanding of overpartition arithmetic properties

Abstract

Recently, Shen (2016) and Alanazi et al. (2016) studied the arithmetic properties of the $\ell$-regular overpartition function $\overline{A}_\ell (n)$, which counts the number of overpartitions of $n$ into parts not divisible by $\ell$. In this note, we will present some new congruences modulo $5$ when $\ell$ is a power of $5$.