Arithmetic Properties of Overpartition Pairs into Odd Parts

Source abstract

In this work, we investigate various arithmetic properties of the function $\overline{pp}_o(n)$, the number of overpartition pairs of $n$ into odd parts. We obtain a number of Ramanujan type congruences modulo small powers of $2$ for $\overline{pp}_o(n)$. For a fixed positive integer $k$, we further show that $\overline{pp}_o(n)$ is divisible by $2^k$ for almost all $n$. We also find several infinite families of congruences for $\overline{pp}_o(n)$ modulo $3$ and two formulae for $\overline{pp}_o(6n+3)$ and $\overline{pp}_o(12n)$ modulo $3$.