Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms
Number Theory
2007-10-10 v4 Representation 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.
Keywords
Cite
@article{arxiv.math/0509077,
title = {Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms},
author = {Andre Reznikov},
journal= {arXiv preprint arXiv:math/0509077},
year = {2007}
}
Comments
Published in JAMS version