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

Oura, Manabu  ,  Ozeki, Michio

86 ( 1 )  , pp.19 - 53 , 2016-04-01 , Springer Verlag
ISSN:0025-5858
NCID:AA00504553
Description
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 (Formula presented.), and calculate the Fourier coefficient (Formula presented.) 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. © 2016 Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg
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http://dspace.lib.kanazawa-u.ac.jp/dspace/bitstream/2297/44886/1/SC-PR-OURA-M-19.pdf

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