Title: Geodesic restrictions of arithmetic eigenfunctions
Speaker: Simon Marshall
Speaker Info: Northwestern
Brief Description:
Special Note:
Abstract:
If X is an arithmetic hyperbolic surface and f is a Hecke-Laplace eigenfunction on X, the Fourier coefficients of f along closed geodesics can be studied both by analytic methods and by using connections with number theory. I will compare the information we get from these two perspectives, and then show how to apply a technique called arithmetic amplification to improve the bound for the L^2 norm of the restriction of f to an arbitrary geodesic segment (which need not be part of a closed geodesic).Date: Monday, November 19, 2012