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

In this paper, we study the partition functions $\overline{R_{\mathrm{\ell }}^{\ast }}(n)$, which count the number of overpartitions of $n$ where the non-overlined parts are $\mathrm{\ell }$-regular for a given $\mathrm{\ell }$. 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.