Eine Bemerkung zur Reduktionstheorie in orthogonalen Gruppen.
Endliche arithmetische Untergruppen der GLn.
Énumération complète des classes de formes parfaites en dimension 7
Le lecteur trouvera ici une description détaillée des méthodes et algorithmes utilisés pour démontrer qu’il n’y a que 33 classes de formes parfaites en dimension 7, ainsi qu’un tableau récapitulatif des résultats.Il trouvera, en particulier, une généralisation de l’algorithme de Voronoï appliquée en profondeur, récursivement, aux faces des domaines
Explicit reduction theory for Siegel modular threefolds.
Extreme copositive quadratic forms
Formes quadratiques encapsulées
Hermite's constant for quadratic number fields.
Inhomogeneous extreme forms
G.F. Voronoi (1868–1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given, but a corresponding result for coverings has been missing. In this paper we bridge the two classical memoirs.By looking at the covering problem from a different perspective, we discover the missing analogue. Instead of trying to find lattices giving economical...
Inhomogeneous Minimum of Indefinite Quadratic Forms in Five Variables of Type (3, 2) or (2, 3): A Conjecture of Watson.
Integral Quadratic Forms, Kac-Moody Algebras, and Fractional Quantum Hall Effect. An ADE- Classification
Invariant measures for actions of unipotent groups over local fields on homogeneous spaces.
Kleine Nullstellen quadratischer Formen in Funktionenkörpern.
La réduction des réseaux. Autour de l'algorithme de Lenstra, Lenstra, Lovász
Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)
Linearly Independent Zeros of Quadratic Forms over Number-Fields.
Low dimensional strongly perfect lattices. II: Dual strongly perfect lattices of dimension 13 and 15.
A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.
Matrix theoretic interpretation of the classical Markoff theory. (L'interprétation matricielle de la théorie de Markoff classique.)
Minkowskische Reduktionsbedingungen für positiv definite quadratische Formen in 5 Variablen.
Note on the degree of concavity of the determinant on sets of positive definite quadratic forms.
On extreme forms in dimension 8
A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for example out of the in dimension ). This is no longer the case in dimension : up to similarity, there...