On the construction of indecomposable positive definite quadratic forms over \({\mathbb Z}\)
type: Item
instance of: scholarly article
title: On the construction of indecomposable positive definite quadratic forms over \({\mathbb Z}\)
zbMATH Open document ID: 0658.10027
author: Fuzu Zhu
author: Youyu Shao
published in: Chinese Annals of Mathematics. Series B
publication date: 1988-01-01T00:00:00Z
review text: Precise results on the existence of indecomposable positive definite lattices over \({\mathbb{Z}}\) with given rank and given discriminant were given by \textit{O. T. O'Meara} [J. Reine Angew. Math. 276, 99--123 (1975; Zbl 0304.10013)] for dimension \(n\geq 10\). (A lattice \(L\) is called decomposable, if it can be expressed as the orthogonal sum of two non-zero sublattices: \(L=M\perp N.)\) This paper extends these results to \(3\leq n\leq 9\), where O'Meara left some cases unsettled. For \(n=2\) a certain criterion for the existence of indecomposable lattices is given by analytic methods.
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 11H55
zbMATH DE Number: 4075176
zbMATH Keywords: indecomposable positive definite quadratic forms
zbMATH Keywords: rank
zbMATH Keywords: discriminant
zbMATH Keywords: existence of indecomposable lattices
reviewed by: Meinhard Peters
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4075176