A generalization of Voronoi's reduction theory and its application
Metric Geometry
2008-04-10 v4 Number Theory
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.
Cite
@article{arxiv.math/0601084,
title = {A generalization of Voronoi's reduction theory and its application},
author = {Mathieu Dutour Sikiric and Achill Schuermann and Frank Vallentin},
journal= {arXiv preprint arXiv:math/0601084},
year = {2008}
}
Comments
31 pages, 2 figures, 2 tables, (v4) minor changes, to appear in Duke Math. J