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New Ramanujan type congruences modulo 5 for overpartitions

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Abstract

Let \(\overline{p}(n)\) denote the number of overpartitions of n. In this paper, we shall show that for \(n\ge 0\),

$$\begin{aligned} \overline{p}(80n+r)\equiv 0\ (\mathrm{mod\ }5), \end{aligned}$$

where \(r=8,52,68\), and 72. In addition, we present a short alternative proof of the congruence

$$\begin{aligned} \overline{p}(40n+35)\equiv 0\ (\mathrm{mod\ }5), \end{aligned}$$

which is conjectured by Hirschhorn and Sellers.

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Acknowledgments

The authors would like to thank the referee for valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Donna Q. J. Dou

  2. School of Science, Jimei University, Xiamen, 361021, People’s Republic of China

    Bernard L. S. Lin

Authors
  1. Donna Q. J. Dou
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  2. Bernard L. S. Lin
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Corresponding author

Correspondence to Bernard L. S. Lin.

Additional information

The first author was supported by the National Natural Science Foundation of China (No. 11201176). The second author was supported by the National Natural Science Foundation of China (No. 11401253), and the Training Program Foundation for Distinguished Young Scholars and Research Talents of Fujian Higher Education (No. JA14171).

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Dou, D.Q.J., Lin, B.L.S. New Ramanujan type congruences modulo 5 for overpartitions. Ramanujan J 44, 401–410 (2017). https://doi.org/10.1007/s11139-016-9782-4

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