The classification of positive definite unimodular lattices over \(\mathbb{Z} [(1+ \sqrt{21})/2]\) (Q2732411)
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scientific article; zbMATH DE number 1623655
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The classification of positive definite unimodular lattices over \(\mathbb{Z} [(1+ \sqrt{21})/2]\) |
scientific article; zbMATH DE number 1623655 |
Statements
7 November 2001
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quaternary quadratic forms
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class numbers
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classification
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0.9325613
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0.9123485
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0.9093117
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0.9074253
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The classification of positive definite unimodular lattices over \(\mathbb{Z} [(1+ \sqrt{21})/2]\) (English)
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By combining Siegel's mass formula and Kneser's neighbour lattice method, the author classifies positive definite unimodular lattices of rank 4 over \(\mathbb{Z}[(1+\sqrt{21})/2]\). There are two genera with three classes (in the even case) resp. nine classes (in the genus of the unit form), and representatives of all these classes are computed.
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