Erzeugung ganzzahliger orthogonaler Gruppen durch Spiegelungen.
Essential dimension: A functorial point of view (after A. Merkurjev).
Estimates for reduced binary forms.
Euclidean quadratic forms and ADC forms: I
Euclidean quadratic forms and ADC forms II: integral forms
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by...
Even Symmetric Sextics.
Even Unimodular 8-Dimensional Quadratic Forms Over Q(...2).
Excellent connections in the motives of quadrics
In this article we prove the conjecture claiming that the motive of a real quadric is the “most decomposable” among anisotropic quadrics of given dimension over all fields. This imposes severe restrictions on the motive of arbitrary anisotropic quadric. As a corollary we estimate from below the rank of indecomposable direct summand in the motive of a quadric in terms of its dimension. This generalizes the well-known Binary Motive Theorem. Moreover, we have the description of the Tate motives involved....
Excellent special orthogonal groups.
Exceptions of integral quadratic forms.
Existence et équidistribution des matrices de dénominateur dans les groupes unitaires et orthogonaux
Soit un groupe défini sur les rationnels, simplement connexe, -quasisimple et compact sur . On étudie des suites de sous-ensembles des points rationnels de définis par des conditions sur leur projection dans le groupe des adèles finies de . Nous montrons dans ce cadre un résultat d’équirépartition vers la probabilité de Haar sur le groupe des points réels. On utilise pour cela des propriétés de mélange de l’action du groupe des points adéliques sur l’espace . Pour illustrer ce résultat,...
Existence of an indecomposable positive quadratic form in a given genus of rank at least 14
Expressing a number as the sum of two coprime squares.
We use hyperbolic geometry to study the limiting behavior of the average number of ways of expressing a number as the sum of two coprime squares. An alternative viewpoint using analytic number theory is also given.
Extension du théorème de Fermat sur les nombres polygones
Extensions algébriques et formes quadratiques
Extensions of classical congruences for parameters in binary quadratic forms
Extrait d'une lettre
Extrait d'une Lettre adressée à M. Besge.
Extrait d'une lettre de M. Ch. Hermite à M. Borchardt sur la réduction des formes quadratiques ternaires.