NTS ABSTRACTFall2024

Back to the number theory seminar main webpage: Main page

Sept 5

Jiaqi Hou

Restrictions of eigenfunctions on arithmetic hyperbolic 3-manifolds

Let X be a compact arithmetic hyperbolic 3-manifold and Y a hyperbolic surface in X. Let f be a Hecke-Maass form on X, which is a joint eigenfunction of the Laplacian and Hecke operators. In this talk, I will present a power saving bound for the period of f along Y over the local bound. I will also present a work in progress on the bound for the L^2 norm of f restricted to Y. Both of the results are based on the method of arithmetic amplification developed by Iwaniec and Sarnak.