Explicit congruences modulo 2048 for overpartitions
type: Item
instance of: scholarly article
title: Explicit congruences modulo 2048 for overpartitions
zbMATH Open document ID: 1468.11217
author: Fanggang Xue
author: Olivia X. M. Yao
published in: The Ramanujan Journal
publication date: 2021-05-06T00:00:00Z
review text: An overpartition of \(n\) is a partition of \(n\) where the first occurrence of each distinct part may be overlined. The number of such overpartitions of \(n\) is denoted by \(\bar p(n)\), Finding congruences modulo powers of primes for overpartitions (as well as other partition functions) is an important field of study in the area. In this paper, the authors find several interesting congruences modulo \(2^{11}\) for \(\bar p(n)\). For instance they show as a special case of Theorem 1.4, that the congruence \[ \bar p(455(2n+1)^2)\equiv 0\pmod{2^{11}} \] holds for all \(n\geq 0\).
reviewed by: Manjil Pratim Saikia
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 7345298
zbMATH Keywords: overpartition
zbMATH Keywords: congruences
MaRDI profile type: Publication
full work available at URL: s11139-019-00204-6
OpenAlex ID: W3002097011
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Wikidata QID: Q126301769
DOI: 10.1007/S11139-019-00204-6
description: scientific article; zbMATH DE number 7345298