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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 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 L is defined by ζ L ( s ) = l Γ L ' [ det ( Q ( l ) ) ] - s , s C where L ' = { l L | det ( Q ( l ) ) 0 } ,...

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