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A generalization of Voronoi's reduction theory and its application

Mathieu Dutour Sikiric·Achill Schuermann·Frank Vallentin
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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 general, the theory is developed for forms which 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 and Nebe. Moreover, we apply it to construct new best known sphere coverings in dimensions 9,..., 15.

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Mathieu Dutour Sikiric, Achill Schuermann, Frank Vallentin. 2007-06-20. A generalization of Voronoi's reduction theory and its application. https://doi.org/10.1215/00127094-2008-003

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