论文信息 - On the Dirichlet—Voronoi cell of unimodular lattices

On the Dirichlet—Voronoi cell of unimodular lattices

This paper consists of two results concerning the Dirichlet-Voronoi cell of a lattice. The first one is a geometric property of the cell of an integral unimodular lattice while the second one gives a characterization of all those lattice vectors of an arbitrary lattice whose multiples by 1/2 are on the boundary of the cell containing the origin. This result is a generalization of a well-known theorem of Voronoi characterizing the so-called relevants of the cell.

Ákos G. Horváth

[1] F. Thorne,et al. Geometry of Numbers , 2017, Algebraic Number Theory.

[2] G. L. Dirichlet. Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. , 1850 .

[3] N. J. A. Sloane,et al. Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[4] U. Schnell. Minimal Determinants and Lattice Inequalities , 1992 .

[5] Georges Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites. , 1908 .

[6] Georges Voronoi. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .