Arithmetic properties of Schur-type overpartitions
type: Item
instance of: scholarly article
title: Arithmetic properties of Schur-type overpartitions
author: Isaac A. Broudy
author: Jeremy Lovejoy
published in: Involve
publication date: 2022-12-20T00:00:00Z
review text: In the theory of partitions there are numerous results like Schur's theorem and the Rogers-Ramanujan identities. It is natural to ask about the parity or other arithmetic properties of the counting functions associated with these identities. In this paper, the authors consider a certain counting function \(S(n)\), which first arose in an overpartition identity related to Schur's partition theorem and a universal mock theta function in [\textit{K. Bringmann} et al., Math. Res. Lett. 23, No. 1, 67--80 (2016; Zbl 1342.05010)]. Using basic facts about modular forms and some elementary algebraic number theory, the authors provide a complete characterization of the parity of this overpartition function in the progressions \(2n+1\), \(4n+2\), and \(8n+4\), a complete characterization of the residue modulo \(4\) in the progressions \(8n + 5\) and \(8n + 7\), and some Ramanujan-type congruences modulo \(5\).
reviewed by: Mircea Merca
Mathematics Subject Classification ID: 11P83
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11P84
zbMATH DE Number: 7635042
zbMATH Keywords: partitions
zbMATH Keywords: overpartitions
zbMATH Keywords: parity
zbMATH Keywords: eta-quotients
zbMATH Keywords: binary quadratic forms
describes a project that uses: OEIS
MaRDI profile type: Publication
full work available at URL: involve.2022.15.489
OpenAlex ID: W4312047783
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DOI: 10.2140/INVOLVE.2022.15.489
description: scientific article; zbMATH DE number 7635042