Representations by unimodular quadratic \(\mathbb{Z}\)-lattices (Q1323412)
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scientific article; zbMATH DE number 567412
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Representations by unimodular quadratic \(\mathbb{Z}\)-lattices |
scientific article; zbMATH DE number 567412 |
Statements
Representations by unimodular quadratic \(\mathbb{Z}\)-lattices (English)
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26 June 1994
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The author's recent results on primitive representations of lattices by unimodular lattices in Am. J. Math. 113, 129-146 (1991; Zbl 0729.11016), J. Number Theory 44, 356-366 (1993; Zbl 0781.11017) are extended. Necessary and sufficient local conditions are given for the primitive representation of a lattice by a unimodular quadratic lattice \(L\) over the integers of a local field (with 2 not ramified), and the number of inequivalent representations, under the action of the orthogonal group O\((L)\), determined. Global results over \(\mathbb{Z}\), for forms corresponding to the Dynkin diagrams, are then obtained via strong approximation.
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dyadic representations
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global representations
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primitive representation of a lattice by a unimodular quadratic lattice
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local field
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number of inequivalent representations
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Dynkin diagrams
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strong approximation
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