Quaternary even positive definite quadratic forms of discriminant \(4p\) (Q1293171)
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scientific article; zbMATH DE number 1309364
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quaternary even positive definite quadratic forms of discriminant \(4p\) |
scientific article; zbMATH DE number 1309364 |
Statements
Quaternary even positive definite quadratic forms of discriminant \(4p\) (English)
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28 June 1999
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Let \(p\equiv 1\bmod 4\), \(p>13\), \(p\in\mathbb{P}\). Let \(G\) be the genus of a quaternary even positive definite \(\mathbb{Z}\)-lattice of discriminant \(4p\) whose 2-adic localization has a proper 2-modular Jordan component. It is shown that the orthogonal group of any lattice from \(G\) is generated by \(-1\) and the symmetries with respect to the roots of the lattice. The class number of \(G\) is computed. Furthermore it is shown that the theta series of degree 2 coming from the classes in \(G\) with nontrivial automorphism groups are linearly independent.
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quaternary quadratic forms
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class numbers of quadratic forms
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0.8482343554496765
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