Number Theory Seminar

Speaker: Jiaqi Hou

Title: Restrictions of Maass forms on arithmetic hyperbolic 3-manifolds

Abstract: Let X be a compact arithmetic hyperbolic 3-manifold and let f be a Hecke-Maass form on X. Using the amplification method, in the spectral aspect we prove a power saving over the local bound by Burq, Gérard, and Tzvetkov for the L^2 norm of f restricted to a totally geodesic surface in X. I will also present a bound for f restricted to geodesic tubes in X, which can be applied to improve the L^p estimate of f by Sogge for 2<p<4.

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