Congruences for ℓ-regular overpartition for ℓ ∈ {5, 6, 8}

Nipen Saikia () and Chayanika Boruah ()
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Nipen Saikia: Rajiv Gandhi University
Chayanika Boruah: Rajiv Gandhi University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 2, 295-308

Abstract: Abstract Let A̅ ℓ(n) denote the number of overpartitions of a non-negative integer n with no part divisible by ℓ, where ℓ is a positive integer. In this paper, we prove infinite family of congruences for A̅ 5(n) modulo 4, A̅ 6(n) modulo 3, and A̅ 8(n) modulo 4. In the process, we also prove some other congruences.

Keywords: ℓ-Regular overpartition; partition congruence; Ramanujan’s theta-function (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0227-6

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