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New congruences for \(\ell \)-regular overpartition pairs

Abstract

Let \(\overline{B}_{\ell }(n)\) denote the number of \(\ell -\) regular overpartition pairs of n. In this paper, we find some Ramanujan like congruences and infinite families of congruences for \(\overline{B}_{\ell }(n)\) for \(\ell \in \{3,4,5,8\}\). For example, for \(n \ge 0\) and \(\alpha \ge 0\), \(\overline{B}_{3}(4^{\alpha +1}(6n+5))\equiv 0\pmod {9}\), \(\overline{B}_{3}(12n+10)\equiv 0\pmod {9}\), \(\overline{B}_{5}(4n+3)\equiv 0\pmod {8}\) and \(\overline{B}_{8}(16n+12)\equiv 0\pmod {16}\).

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Correspondence to C. Shivashankar.

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Shivashankar, C., Gireesh, D.S. New congruences for \(\ell \)-regular overpartition pairs. Afr. Mat. 33, 82 (2022). https://doi.org/10.1007/s13370-022-01018-4

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  • DOI: https://doi.org/10.1007/s13370-022-01018-4

Keywords

  • Congruences
  • Theta function
  • Overpartition pair
  • \(\ell -\) regular partition

Mathematics Subject Classification

  • 11P83
  • 05A15
  • 05A17