New arithmetic properties for overpartitions where nonoverlined parts are $\ell$-regular

Abstract

In this paper, we study the partition functions $\overline{R_\ell^\ast}(n)$, which count the number of overpartitions of $n$ where the non-overlined parts are $\ell$-regular for a given $\ell$. Using elementary techniques, as well as the theory of modular forms, we establish several new arithmetic properties, including infinite families of congruences for these functions.