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

Research paper by Andre Reznikov

Indexed on: 10 Oct '07Published on: 10 Oct '07Published in: Mathematics - Number Theory



Abstract

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.