SOME IDENTITIES OF OVERPARTITION PAIRS INTO ODD PARTS

Abstract

Recently, Bernard L.S.~Lin has studied various arithmetic properties of the function $\overline{pp_0}(n)$, the number of overpartition pairs of $n$ into odd parts. In particular, he has obtained a number of Ramanujan-type congruences modulo 3 and modulo powers of 2. In this paper, we give proof of some of these congruences and find some other interesting congruences by employing elementary generating function dissection techniques.