Nearly unimodular quadratic forms
type: Item
instance of: scholarly article
title: Nearly unimodular quadratic forms
zbMATH Open document ID: 0842.11012
DOI: 10.2307/2118555
author: Larry J. Gerstein
published in: Annals of Mathematics. Second Series
publication date: 1996-07-28T00:00:00Z
review text: A \(\mathbb Z\)-lattice \(L\) is called nearly unimodular if it has a Gram matrix of the form \[ \left( \begin{smallmatrix} a_1 &1 \\ 1 &a_2 & \ddots\\ & \ddots &\ddots \\ &&&a_{n-1} &1\\ &&&1 &a_n \end{smallmatrix} \right)=: [a_1, \dots, a_n ]=: A \] (then we denote \(L\cong A)\). The main result is the following classification theorem: Let \(A= [a_1, \dots, a_n ]\) and \(B= [b_1, \dots, b_n ]\). Suppose \(L\) and \(M\) are positive definite nearly unimodular \(\mathbb Z\)-lattices with \(L\cong A\) and \(M\cong B\). Then \(L\) is isometric to \(M\) if and only if \(B= A\) or \(B= [a_n, \dots, a_1]\).
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 837032
zbMATH Keywords: nearly unimodular quadratic forms
zbMATH Keywords: nearly unimodular lattices
reviewed by: Meinhard Peters
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118555
OpenAlex ID: W2312573283
description: scientific article; zbMATH DE number 837032