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Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.

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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