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Overpartition function modulo powers of 2

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Abstract

Let \(\overline{p}(n)\) denote the number of overpartitions of n. Recently, congruences modulo powers of 2 for \(\overline{p}(n)\) were widely studied. In this paper, we prove several new infinite families of congruences modulo powers of 2 for \(\overline{p}(n)\). For example, for \(\alpha \ge 1\) and \(n\ge 0\),

$$\begin{aligned} \overline{p}(8\cdot 3^{4\alpha +4}n+5\cdot 3^{4\alpha +3})\equiv 0 \quad (\mathrm{mod}\,\,{2^8}). \end{aligned}$$

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Authors and Affiliations

  1. Department of Basic Subjects Teaching, Changchun Architecture & Civil Engineering College, Changchun, 130607, Jilin, People’s Republic of China

    Xue Yang & Su-Ping Cui

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

    Bernard L. S. Lin

Authors
  1. Xue Yang
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  2. Su-Ping Cui
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  3. Bernard L. S. Lin
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Corresponding author

Correspondence to Su-Ping Cui.

Additional information

The first author was supported by Research and Practice of Improving the Teaching Effectiveness of Higher Mathematics in Private College[GH14662]. The third author was supported by the Training Program Foundation for Distinguished Young Scholars and Research Talents of Fujian Higher Education (No. JA14171).

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Yang, X., Cui, SP. & Lin, B.L.S. Overpartition function modulo powers of 2. Ramanujan J 44, 89–104 (2017). https://doi.org/10.1007/s11139-016-9784-2

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