Configurations of rank-\(40r\) extremal even unimodular lattices \((r=1,2,3)\) (Q1011960)
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| Language | Label | Description | Also known as |
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| English | Configurations of rank-\(40r\) extremal even unimodular lattices \((r=1,2,3)\) |
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Configurations of rank-\(40r\) extremal even unimodular lattices \((r=1,2,3)\) (English)
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14 April 2009
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It is shown that any extremal even unimodular lattice \(L\) of rank \(40r\) with \(r=1,2,3\) is generated by its vectors of square length \(4r\) and \(4r+2\). The authors extend \textit{M. Ozeki}'s method who proved the result for \(r=1\) using theta series with harmonic coefficients [Rocky Mt. J. Math. 19, No. 3, 847--862 (1989; Zbl 0706.11018)].
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even unimodular lattices
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extremal lattices
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harmonic theta series
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spherical designs
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