Examples of even unimodular extremal lattices of rank 40 and their Siegel theta-series of degree 2
type: Item
instance of: scholarly article
title: Examples of even unimodular extremal lattices of rank 40 and their Siegel theta-series of degree 2
zbMATH Open document ID: 0638.10031
DOI: 10.1016/0022-314X(88)90059-5
author: Michio Ozeki
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: An even unimodular lattice in n-dimensional Euclidean space is called extremal if its minimum attains the upper bound \(2[n/24]+2;\) all such lattices have the same theta series of degree 1. One knows that for \(n=40\) there are more than \(10^{50}\) classes of extremal lattices [\textit{M. Peters}, Bull. Lond. Math. Soc. 15, 18-20 (1983; Zbl 0506.10016)]. In the present paper three of these are found to have different Siegel theta series of degree 2, and the question is posed whether all the classes can be distinguished in this way.
Mathematics Subject Classification ID: 11H55
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 4040003
zbMATH Keywords: [40,20]-codes
zbMATH Keywords: self-dual codes
zbMATH Keywords: unimodular lattice
zbMATH Keywords: extremal lattices
zbMATH Keywords: Siegel theta series of degree 2
reviewed by: Heinz-Georg Quebbemann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4040003