06-22
A generalization of Voronoi\'s reduction theory and its application
by Mathieu Dutour Sikiric; Achill Schürmann; Frank Vallentin
Preprint series: 06-22, Preprints
- MSC:
- 11H55 Quadratic forms (reduction theory, extreme forms, etc.)
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 $9,\dots,15$.
Keywords: Voronoi reduction, totally real thin number fields, sphere coverings
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