A generalization of Voronoi's reduction theory and its application

Sikiric, Mathieu Dutour; Schuermann, Achill; Vallentin, Frank

A generalization of Voronoi's reduction theory and its application

Authors

Sikiric, Mathieu Dutour

Schuermann, Achill

Vallentin, Frank

Description

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.
31 pages, 2 figures, 2 tables, (v4) minor changes, to appear in Duke Math. J