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

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

2005-09-04

arxiv.org/abs/math/0509077v4

Mathematics

Number Theory

Published in JAMS version

Scientific paper

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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