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.
Covering space with convex bodies
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...
Definite unimodular lattices having an automorphism of given characteristic polynomial.
Designs, groups and lattices
The notion of designs in Grassmannian spaces was introduced by the author and R. Coulangeon, G. Nebe, in [3]. After having recalled some basic properties of these objects and the connections with the theory of lattices, we prove that the sequence of Barnes-Wall lattices hold -Grassmannian designs. We also discuss the connections between the notion of Grassmannian design and the notion of design associated with the symmetric space of the totally isotropic subspaces in a binary quadratic space, which...
Diffeomorphisms of a K3 Surface.
Diophantine approximation and certain sequences of lattices
Diophantine approximation and special Liouville numbers
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers . The approach relies on results on the connection between the set of all -adic expansions () of and their associated approximation constants. As an application, explicit construction of real numbers with prescribed approximation properties are deduced and illustrated by Matlab plots.
Diphantine Approximation with Square-free Numbers.
Discrete and dense subgroup problems. (Problemas con subgrupos discretos y subgroupos densos.)
Distribution of lattice points on hyperbolic surfaces
Let two lattices have the same number of points on each hyperbolic surface . We investigate the case when Λ’, Λ” are sublattices of of the same prime index and show that then Λ’ and Λ” must coincide up to renumbering the coordinate axes and changing their directions.
Economical Coverings of Sets of Lattice Points.
Edge matrices for the fundamental cone.
Ein Extremalproblem für Gitterpunkte.
Ein isoradiales Problem mit Nebenbedingung im triagonalen Gitter
Ein Übertragungsprinzip für konvexe Körper