Congruences for cubic partition pairs modulo powers of 3
type: Item
instance of: scholarly article
title: Congruences for cubic partition pairs modulo powers of 3
zbMATH Open document ID: 1396.05011
author: Bernard L. S. Lin
author: Liuquan Wang
author: Ernest X. W. Xia
published in: The Ramanujan Journal
publication date: 2018-07-20T00:00:00Z
review text: In the paper under review, the authors establish congruences for \(b(n)\) modulo arbitrary powers of three, where the partition function \(b(n)\) enumerates the number of cubic partition pairs of \(n\) and has generating function \[ \sum_{n=0}^{\infty}b(n)q^n=\frac{1}{(q;q)_{\infty}^2(q^2;q^2)_{\infty}^2}. \] For instance, they show that for integers \(j\geq 2\) and \(n\geq 0\), \[ b\left(3^{2j}n+\frac{3^{2j+1}+1}{4}\right)\equiv 0\,\pmod {3^{2j+1}}. \] The authors also prove some conjectures for \(b(n)\) modulo \(81\) and \(243\), proposed by the first author in [J Number Theory 171, 31--42 (2017; Zbl 1357.11105)].
reviewed by: Ricardo Mamede
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 6908982
zbMATH Keywords: cubic partition pairs
zbMATH Keywords: congruences
zbMATH Keywords: Ramanujan's cubic continued fraction
MaRDI profile type: Publication
full work available at URL: s11139-017-9955-9
OpenAlex ID: W2769773137
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DOI: 10.1007/S11139-017-9955-9
description: scientific article; zbMATH DE number 6908982