2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139673We 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.Published in JAMS versionNumber TheoryRepresentation Theory11F67, 22E45, 11F70, 11M26text