N. Sujatha

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

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 $n\geq0$ we prove that $$\overline{p}_{4}(32n+28)\equiv 0 \pmod{512}.$$