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New congruences modulo $5$ for overpartitions

Volume 145 / 2016

Tao Yan Zhao, Lily J. Jin Colloquium Mathematicum 145 (2016), 285-290 MSC: Primary 05A17; Secondary 11P83. DOI: 10.4064/cm6744-1-2016 Published online: 8 July 2016


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 $\bar{p}(4n)$.


  • Tao Yan ZhaoDepartment of Mathematics
    Jiangsu University
    Zhenjiang, Jiangsu 212013, P.R. China
  • Lily J. JinSchool of Mathematics
    College of Taizhou
    Nanjing Normal University
    Taizhou, Jiangsu 225300, P.R. China

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