Arithmetic properties of overpartition pairs into odd parts

Lishuang Lin¹

¹Jimei University

The electronic journal of combinatorics, Tome 19 (2012) no. 2

Résumé

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 $3$.

Détail

DOI : 10.37236/2274

Classification : 05A17, 11P83
Mots-clés : congruence, modular forms