On the parity of the number of lattice points in certain tetrahedra.
On the proof of Humbert's volume formula.
On the representation of integers as sums of triangular numbers.
On the section of a lattice–covering of balls
On the S-Euclidean minimum of an ideal class
We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...
On theta series vanishing at ∞ and related lattices
One-class genera of positive quaternary quadratic forms
Orbits in the Leech lattice.
Orthogonal systems in vector spaces over finite fields.
Parametric geometry of numbers and applications
Perfect Delaunay polytopes in low dimensions.
Periodic sphere packings and the Wulff-shape.
Points entiers dans les polyèdres convexes
Points entiers dans les polytopes convexes
Points extrémaux d'un convexe compact de Rn appartenant à un réseau
Points frontières de certains compacts convexes appartenant à un réseau, dans et
Polar lattices from the point of view of nuclear spaces.
The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.
Primitive minima of positive definite quadratic forms
The main purpose of the reduction theory is to construct a fundamental domain of the unimodular group acting discontinuously on the space of positive definite quadratic forms. This fundamental domain is for example used in the theory of automorphic forms for GLₙ (cf. [11]) or in the theory of Siegel modular forms (cf. [1], [4]). There are several ways of reduction, which are usually based on various minima of the quadratic form, e.g. the Korkin-Zolotarev method (cf. [10], [3]), Venkov's method...
Propositions arithmétiques tirées de la théorie de la fonction exponentielle. (Extrait d'une Lettre adressée à M. Hermite)
Quadratic Forms and the ?-Invariant. II.