New congruences modulo 5 for overpartitions (Q2833647)

An over partition of the positive integer \(n\) is a partition of \(n\) where the first occurence of each distinct part may be overlined. Let \(\bar{p}(n)\) denote the number of overpartitions of \(n\). In this paper, the authors establish five new congruences modulo 5 using the generating function for \(\bar{p}(n)\) and some theta function identities due to Ramanujan. For instance, they show that \(\sum_{i+j=n}\bar{p}(80i+32)\bar{p}(80j+28) \) \(\equiv\sum_{i+j=n}\bar{p}(80i+12)\bar{p}(80j+48) (\mod 5)\).