On Siegel's Lemma.
On ternary cubic forms.
On the gaps of the Lagrange spectrum
On the Gaussian Markoff spectrum.
On the Lower Markov Spectrum.
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...
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...
Quaternary quadratic forms and an associated lattice constant
Radiography of perfect lattices. (Radiographie des réseaux parfaits.)
Strongly modular lattices with long shadow
This article classifies the strongly modular lattices with longest and second longest possible shadow.
Structure of the Markoff spectrum below √12
Sur la classification des réseaux parfaits de dimension
En utilisant des méthodes de Watson, nous donnons une courte démonstration de la classification (due à Korkine et Zolotareff ) des réseaux parfaits de dimension 5. Des considérations d'indice nous conduisent à nous intéresser à trois classes de réseaux, dont chacune contient précisément un réseau parfait.
Sur les formes quadratiques positives quaternaires. (Zus. mit G. Zolotareff)
Sur les formes quadratiques positives. (Zus. Mit S. Zolotareff)
Sur les formes quadratiques ternaires indéfinies
Sur les formes quadratiques (Zus. mit Zolotareff)
Systoles of arithmetic surfaces and the Markoff spectrum.
The inhomogeneous minima of a sequence of symmetric Markov forms
The Lehmus inequality.
The Markoff spectrum