Cayley orders
Characerization of a class of distance regular graphs.
Characteristic vectors of unimodular lattices which represent two
We improve the known upper bound of the dimension of an indecomposable unimodular lattice whose shadow has the third largest possible length, .
Classification des formes quadratiques réelles: un contre-exemple à la finitude
1. Introduction. On doit à G. Voronoï [Vo] un algorithme de classification complète des formes quadratiques parfaites. Il est dès lors possible, en principe, de déterminer en un temps fini la constante d'Hermite γₙ, qui décrit dans ℝⁿ la densité maximale des empilements de sphères en réseau. L'énorme complexité de l'algorithme lui donne une limite naturelle: il semble actuellement impensable de dépasser la dimension 8, où les explorations ont déjà fourni des milliers de formes...
Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order.
Codes, lattices, and Steiner systems.
Compactification de l’espace des modules des variétés abéliennes principalement polarisées
Les variétés abéliennes principalement polarisées admettent un espace des modules grossier qu’on sait compactifier de plusieurs façons (compactification de Satake, compactifications toroïdales). Cependant, le problème s’est posé de construire une compactification “modulaire”en termes d’objets géométriques qui permettent de décrire les points du bord. On souhaite aussi compactifier l’application de Torelli qui à chaque courbe algébrique, projective et lisse, associe sa jacobienne. L’exposé présente...
Computations of cyclotomic lattices.
Computing the Ehrhart Polynomial of a Convex Lattice Polytope.
Concernant la relation de distribution satisfaite par la fonction ...associé à un réseau complexe.
Configurations of rank- extremal even unimodular lattices ()
We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
Continuity Properties of Voronoi Domains.
Corrigenda: ‘On systems of linear inequalities’
There are two mistakes in the referred paper. One is ridiculous and one is significant. But none is serious.
Counting problems and semisimple groups.
Covering space with convex bodies
Coverings Sets for Plane Lattices.
Cyclic overlattices, I
Cyclic overlattices, II (Diophantine approximation and sums of roots of unity)
Cyclotomic modular lattices
Several interesting lattices can be realised as ideal lattices over cyclotomic fields : some of the root lattices, the Coxeter-Todd lattice, the Leech lattice, etc. Many of these are modular in the sense of Quebbemann. The aim of the present paper is to determine the cyclotomic fields over which there exists a modular ideal lattice. We then study an especially simple class of lattices, the ideal lattices of trace type. The paper gives a complete list of modular ideal lattices of trace type defined...
Cyclotomic quadratic forms
Voronoï ’s algorithm is a method for obtaining the complete list of perfect -dimensional quadratic forms. Its generalization to -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of -perfect forms ( is a finite subgroup of . We study the standard, -dimensional irreducible representation of the cyclic group of order , and give the, often new, densest -forms. Perfect cyclotomic forms are completely classified for and for...