New congruences modulo $5$ for overpartitions
Volume 145 / 2016
Colloquium Mathematicum 145 (2016), 285-290
MSC: Primary 05A17; Secondary 11P83.
DOI: 10.4064/cm6744-1-2016
Published online: 8 July 2016
Abstract
Let $\bar{p}(n)$ denote the number of overpartitions of $n$. Recently, several congruences for $\bar{p}(n)$ modulo 5 have been proved by Chen and Xia, by Chen, Sun, Wang and Zhang, and by Wang. In this paper, we prove new congruences for $\bar{p}(n)$ modulo 5 by using some theta function identities and the generating function for $\bar{p}(4n)$.
