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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.
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Mar 2, 2016
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