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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, 791 112, Arunachal Pradesh, India

    Nipen Saikia & Chayanika Boruah

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  1. Nipen Saikia
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  2. Chayanika Boruah
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Correspondence to Nipen Saikia.

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Saikia, N., Boruah, C. Congruences for ℓ-regular overpartition for ℓ ∈ {5, 6, 8}. Indian J Pure Appl Math 48, 295–308 (2017). https://doi.org/10.1007/s13226-017-0227-6

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  • DOI: https://doi.org/10.1007/s13226-017-0227-6

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