On Gauss's proof of Seeber's Theorem.
On perfect forms in six variables.
On the computation of Hermite-Humbert constants for real quadratic number fields
We present algorithms for the computation of extreme binary Humbert forms in real quadratic number fields. With these algorithms we are able to compute extreme Humbert forms for the number fields and . Finally we compute the Hermite-Humbert constant for the number field .
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...
One-class genera of positive quaternary quadratic forms
Perfect Delaunay polytopes in low dimensions.
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...
Quadratic Forms and the ?-Invariant. II.
Quadratic Forms Which Have Only Large Zeros.
Rank forms, closed zones and laminae
For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank quadratic forms which are extreme rays for the corresponding -type domain.
Reduction Theory for Fuchsian Groups.
Remarques sur quelques propositions dues à M. Hermite
Simultaneously good bases of a lattice and its reciprocal lattice.
Small Linearly Independent Zeros of Quadratic Forms.
Sublattices of certain Coxeter lattices
In this paper, we describe the sublattices of some lattices, extending previous results of [Ber]. Our description makes intensive use of graphs.
Sur les formes quadratiques binaires indéfinies
Sur les formes quadratiques positives quaternaires. (Zus. mit G. Zolotareff)
Sur les formes quadratiques positives. (Zus. Mit S. Zolotareff)
Sur les formes quadratiques (Zus. mit Zolotareff)
Sur les propriétés des nombres entiers qui sont dérivées de l'intuition de l'espace