Joint Princeton University/Rutgers/Institute for Advanced Study

NUMBER THEORY SEMINAR
for 4/10/2003

Stephen Miller
Rutgers University

Automorphic Distributions and Summation Formulas

Abstract

The talk will center on the analysis of the distributional boundary values of automorphic forms, and some applications of this theory to GL(3,Z)\GL(3,R). Foremost among these is a formula ala Poisson/Voronoi for sums weighted by the Fourier coefficients/Hecke eigenvalues of automorphic forms. This can be used to demonstrate cancellation in such sums, and was an ingredient of the recent sharp estimate of Sarnak-Watson for L_4 norms of Laplace eigenfunctions. I plan to discuss the problem of finding cancellation in sums of the form a_{n,1} exp(2 pi i n alpha), where alpha is irrational. (joint work with Wilfried Schmid).