PACHE, Claude

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

PACHE, Claude
Théorie des Nombres et Algorithmique Arithmétique [A2X]

Idioma

Document de travail - Pré-publication

Resumen en inglés

A well known theorem of Voronoi caracterizes extreme quadratic forms and Euclidean lattices, that is those which are local maxima for the Hermite function, as perfect and eutactic. This caracterization has been extended in various cases, such that family of lattices, sections of lattices, Humbert forms, etc. Moreover, there is a criterion for extreme lattices, discovered by Venkov, formulated in terms of spherical designs which has been extended in the case of Grassmannians and sections of lattices. In this article, we define a general frame, in which there is a ``Voronoi characterization'', and a ``Venkov criterion'' through an appropriate notion of design. This frame encompasses many interesting situations in which a ``Voronoi characterization'' has been proved. We also discuss the question of extremality relatively to the Epstein zeta function, and we extend to our frame a characterization of final zeta-extremality formulated by Delone and Ryshkov and a criterion in terms of designs found by Coulangeon.< Leer menos

Palabras clave en portugués

quadratic form

extreme form

design

Epstein zeta function

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251