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Distinguishing Siegel theta series of degree 4 for the 32-dimensional even unimodular extremal lattices

Distinguishing Siegel theta series of degree 4 for the 32-dimensional even unimodular extremal... In a previous paper we showed that if one particular Fourier coefficient of the Siegel theta series of degree 4 for a 32-dimensional even unimodular extremal lattice is known then the other Fourier coefficients of the series are in principle determined. In this paper we choose the quaternary positive definite symmetric matrix $$\mathfrak {T}_{40}$$ T 40 , and calculate the Fourier coefficient $$a(\mathfrak {T}_{40},\mathcal{L}_{32})$$ a ( T 40 , L 32 ) of the Siegel theta series of degree 4 associated with the five even unimodular extremal lattices which come from the five binary self-dual extremal [32,16,8] codes. As a result we can show that the five Siegel theta series of degree 4 associated with the five 32-dimensional even unimodular extremal lattices are distinct. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

Distinguishing Siegel theta series of degree 4 for the 32-dimensional even unimodular extremal lattices

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-016-0120-y
Publisher site
See Article on Publisher Site

Abstract

In a previous paper we showed that if one particular Fourier coefficient of the Siegel theta series of degree 4 for a 32-dimensional even unimodular extremal lattice is known then the other Fourier coefficients of the series are in principle determined. In this paper we choose the quaternary positive definite symmetric matrix $$\mathfrak {T}_{40}$$ T 40 , and calculate the Fourier coefficient $$a(\mathfrak {T}_{40},\mathcal{L}_{32})$$ a ( T 40 , L 32 ) of the Siegel theta series of degree 4 associated with the five even unimodular extremal lattices which come from the five binary self-dual extremal [32,16,8] codes. As a result we can show that the five Siegel theta series of degree 4 associated with the five 32-dimensional even unimodular extremal lattices are distinct.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Mar 2, 2016

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