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Currently displaying 1 – 2 of 2

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Représentations des algèbres de rang 2 et fonctions zêta associées

Dehbia Achab — 1995

Annales de l'institut Fourier

Dans un travail précédent nous avons défini et étudié la fonction zêta associée à une représentation d’une algèbre de Jordan euclidienne déployée et à un réseau dans l’espace de la représentation. Nous avons démontré la convergence dans un demi-plan, établi l’existence d’un prolongement méromorphe et d’une équation fonctionnelle scalaire. Cette fonction est une généralisation de la fonction zêta de Koecher; elle est donnée dans son domaine de convergence, par une série qui somme sur certains éléments...

Zeta functions of Jordan algebras representations

Dehbia Achab — 1995

Annales de l'institut Fourier

This work is about a generalization of Kœcher’s zeta function. Let $V$ be an Euclidean simple Jordan algebra of dimension $n$ and rank $m$ , $E$ an Euclidean space of dimension $N$ , $ϕ$ a regular self-adjoint representation of $V$ in $E$ , $Q$ the quadratic form associated to $ϕ$ , $Ω$ the symmetric cone associated to $V$ and $G (Ω)$ its automorphism group $G (Ω) = {g \in G L (V) | g (Ω) = Ω} .$ ( $H_{1}$ ) Assume that $V$ and $E$ have $Q$ -structures $V_{Q}$ and $E_{Q}$ respectively and $ϕ$ is defined over $Q$ . Let $L$ be a lattice in $E_{Q}$ . The zeta series associated to $ϕ$ and...

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