New congruences modulo 5 for overpartitions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1358.05026
author: Tao Yan Zhao
author: Lily J. Jin
published in: Colloquium Mathematicum
publication date: 2016-11-18T00:00:00Z
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 6654804
zbMATH Keywords: overpartitions
zbMATH Keywords: congruences
MaRDI profile type: Publication
full work available at URL: cm6744-1-2016
OpenAlex ID: W2471076299
DOI: 10.4064/CM6744-1-2016
title: New congruences modulo 5 for overpartitions
review text: An over partition of the positive integer \(n\) is a partition of \(n\) where the first occurence of each distinct part may be overlined. Let \(\bar{p}(n)\) denote the number of overpartitions of \(n\). In this paper, the authors establish five new congruences modulo 5 using the generating function for \(\bar{p}(n)\) and some theta function identities due to Ramanujan. For instance, they show that \(\sum_{i+j=n}\bar{p}(80i+32)\bar{p}(80j+28) \) \(\equiv\sum_{i+j=n}\bar{p}(80i+12)\bar{p}(80j+48) (\mod 5)\).
reviewed by: Ljuben Mutafchiev
description: scientific article; zbMATH DE number 6654804