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Three finiteness theorems for \(G\)-forms. (Trois théorèmes de finitude pour les \(G\)-formes.) (French) Zbl 0843.11032

The author shows that for a finite subgroup \(G\) of \(Gl_n (\mathbb{Z})\) there is, up to \(G\)-equivalence, only a finite number of \(G\)-perfect (or \(G\)-eutactic, \(G\)-extreme) forms. This generalizes in a way classical results by Voronoi on perfect and eutactic (quadratic) forms.
Reviewer: J.M.Wills (Siegen)

MSC:

11H55 Quadratic forms (reduction theory, extreme forms, etc.)
11H31 Lattice packing and covering (number-theoretic aspects)
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References:

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