Gelfand pairs and bounds for various Fourier coefficients of automorphic functions

Abstract

We explain how the uniqueness of certain invariant functionals on irreducible unitary representations leads to non-trivial spectral identities between various periods of automorphic functions. As an example of an application ofthese identities, we deduce a non-trivial bounds for the corresponding unipotent and spherical Fourier coefficients of Maass forms.

Date of Award	2006
Original language	American English
Awarding Institution	Research Institute for Mathematical Sciences, Department of Mathematics