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Une nouvelle interprétation de la formule des traces de Selberg. (A new interpretation of Selberg’s trace formula). (French) Zbl 0652.10024

From the abstract: “Selberg’s trace formula relates the two spectra of a hyperbolic compact Riemann surface: the length spectrum and the eigenvalues of the Laplacian. Rather than using a Fourier transform as usual, we define a new meromorphic function whose properties encompass both spectra. This function satisfies a functional equation generalizing classical results about the tangent function (connected to the Poisson formula). As an application we derive Selberg’s trace formula for functions not covered by the usual proof.”
Reviewer: M.Burger

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
35P20 Asymptotic distributions of eigenvalues in context of PDEs
53C22 Geodesics in global differential geometry
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