Characteristic vectors of unimodular lattices which represent two (Q933201)
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scientific article; zbMATH DE number 5302782
| Language | Label | Description | Also known as |
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| English | Characteristic vectors of unimodular lattices which represent two |
scientific article; zbMATH DE number 5302782 |
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Characteristic vectors of unimodular lattices which represent two (English)
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21 July 2008
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The author improves the known upper bound of the dimension \(n\) of an indecomposable unimodular lattice \(L\) whose shadow has the third largest possible length, \(s=n-16\) to \(n\leq 89\). \textit{G. Nebe} and \textit{B. Venkov} [J. Number Theory 99, No. 2, 307--317 (2003; Zbl 1081.11049)] proved that if \(L\) has no roots and \(s=n-16\), then \(\text{rank}(L)\leq 46\). This bound is attained by \(L=O_{23}\perp O_{23}\) where \(O_{23}\) is the shorter Leech lattice.
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