Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms

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We use the uniqueness of various invariant functionals on irreducible unitary representations of PGL(2,R) in order to deduce the classical Rankin-Selberg identity for the sum of Fourier coefficients of Maass cusp forms and its new anisotropic analog. We deduce from these formulas non-trivial bounds for the corresponding unipotent and spherical Fourier coefficients of Maass forms. As an application we obtain a subconvexity bound for certain L-functions. Our main tool is the notion of Gelfand pair.
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Number Theory, Representation Theory, 11F67, 22E45, 11F70, 11M26

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http://salesiana.dossiersoluciones.com/handle/123456789/139673

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509077
 http://arxiv.org/abs/math/0509077

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arXiv