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

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dc.creatorReznikov, Andre
dc.date2005-09-04
dc.date2007-10-10
dc.date.accessioned2026-07-07T08:35:12Z
dc.date.available2026-07-07T08:35:12Z
dc.descriptionWe 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.
dc.descriptionPublished in JAMS version
dc.identifierhttps://arxiv.org/abs/math/0509077
dc.identifierhttp://arxiv.org/abs/math/0509077
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139673
dc.subjectNumber Theory
dc.subjectRepresentation Theory
dc.subject11F67, 22E45, 11F70, 11M26
dc.titleRankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms
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