Three classical results on representations of a number
type: Item
instance of: scholarly article
title: Three classical results on representations of a number
zbMATH Open document ID: 0927.11018
published in: Séminaire Lotharingien de Combinatoire
publication date: 1999-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/120032
full work available at URL: s42hirsch.html
review text: The number of representations of a positive integer in the forms \(x^2+3y^2,\) \(x^2+xy+y^2,\) with \(x,y\in \mathbb Z\) and \((x^2+x)/2+3(y^2+y)/2\) with \(x,y\in \mathbb {Z}^+\) and various corresponding formulae as classical results are well-known at present. However, there exist also different methods of investigating this problem. The expressions of the formulae for the representations show the close relations between them. The author proves one known formulae of such type, namely a functional analog with the corresponding \(q\)-series and demonstrates the connections between them in such a way.
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11D85
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 1301082
zbMATH Keywords: number of representations
zbMATH Keywords: number of divisors
zbMATH Keywords: \(q\)-series
author: Michael D. Hirschhorn
reviewed by: Guram Gogishvili
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1301082