New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions
type: Item
instance of: scholarly article
title: New Ramanujan-like congruences modulo powers of 2 and 3 for overpartitions
zbMATH Open document ID: 1275.11136
author: Olivia X. M. Yao
author: Ernest X. W. Xia
published in: Journal of Number Theory
publication date: 2013-04-15T00:00:00Z
review text: Let \(\overline{p}(n)\) denote the number of overpartitions of \(n\). There are five theorems in the paper, containing \(13\) congruences. The following are typical examples: \[ \begin{aligned} \overline{p}(24n+19) &\equiv 0 \pmod{27}, \\ \overline{p}(72n+69) &\equiv 0 \pmod{32}, \\ \overline{p}(48n+2) &\equiv \begin{cases} 4 \pmod{8}, &\text{if \(n = k(3k \pm 1)/2\)}, \\ 0 \pmod{8}, &\text{otherwise}. \end{cases} \end{aligned} \] The proofs are elementary, beginning with known infinite product generating functions for \(\overline{p}(3n+x)\), \(0 \leq x \leq 2\), and then applying a variety of \(2\)-dissections.
reviewed by: Jeremy Lovejoy
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 6154099
zbMATH Keywords: congruences
zbMATH Keywords: overpartitions
zbMATH Keywords: 2-dissection
MaRDI profile type: Publication
full work available at URL: j.jnt.2012.11.002
OpenAlex ID: W1982956313
DOI: 10.1016/J.JNT.2012.11.002
description: scientific article; zbMATH DE number 6154099