Arithmetic properties of the 2-color overpartition function ${\overline{p}}_{\ell }(n)$

Abstract

We derive general families of Ramanujan-type congruences for the function ${\overline{p}}_{\ell }(n)$, which counts the $2$-color overpartitions of $n$ in which one of the colors appears only in parts that are multiples of $\ell$. For example, for all $n\ge 0$ we prove that $${\overline{p}}_4(32n+28)\equiv 0(\mathrm{mod}512).$$