A generalization of Voronoi's reduction theory and its application
Sikirić, Mathieu Dutour ; Schürmann, Achill ; Vallentin, Frank
Duke Math. J., Tome 141 (2008) no. 1, p. 127-164 / Harvested from Project Euclid
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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 $9,\dots,15$
Publié le : 2008-03-15
Classification:  11H55,  52C17 
@article{1206642066,
     author = {Sikiri\'c, Mathieu Dutour and Sch\"urmann, Achill and Vallentin, Frank},
     title = {A generalization of Voronoi's reduction theory and its application},
     journal = {Duke Math. J.},
     volume = {141},
     number = {1},
     year = {2008},
     pages = { 127-164},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1206642066}
}

Sikirić, Mathieu Dutour; Schürmann, Achill; Vallentin, Frank. A generalization of Voronoi's reduction theory and its application. Duke Math. J., Tome 141 (2008) no. 1, pp.  127-164. http://gdmltest.u-ga.fr/item/1206642066/