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15 March 2008 A generalization of Voronoi's reduction theory and its application
Mathieu Dutour Sikirić, Achill Schürmann, Frank Vallentin
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Duke Math. J. 142(1): 127-164 (15 March 2008). DOI: 10.1215/00127094-2008-003

Abstract

We consider Voronoi's reduction theory of positive definite quadratic forms, which is based on Delone subdivision. We extend it to forms and Delone subdivisions having a prescribed symmetry group. Even more generally, the theory is developed for forms that are restricted to a linear subspace in the space of quadratic forms. We apply the new theory to complete the classification of totally real, thin algebraic number fields which was recently initiated by Bayer-Fluckiger [BF] and Bayer-Fluckiger and Nebe [BFN]. Moreover, we apply it to construct new best-known sphere coverings in dimensions 9,,15.

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Mathieu Dutour Sikirić. Achill Schürmann. Frank Vallentin. "A generalization of Voronoi's reduction theory and its application." Duke Math. J. 142 (1) 127 - 164, 15 March 2008. https://doi.org/10.1215/00127094-2008-003

Information

Published: 15 March 2008
First available in Project Euclid: 27 March 2008

zbMATH: 1186.11040
MathSciNet: MR2397885
Digital Object Identifier: 10.1215/00127094-2008-003

Subjects:
Primary: 11H55
Secondary: 52C17

Rights: Copyright © 2008 Duke University Press

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Vol.142 • No. 1 • 15 March 2008
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