Geodesic restrictions of arithmetic eigenfunctions

Abstract

Let X be an arithmetic hyperbolic surface arising from a quaternion division algebra over Q. Let ψ be a Hecke–Maass form on X, and let ℓ be a geodesic segment. We obtain a power saving over the local bound of Burq, Gérard, and Tzvetkov for the L2-norm of ψ restricted to ℓ, by extending the technique of arithmetic amplification developed by Iwaniec and Sarnak. We also improve the local bounds for various Fourier coefficients of ψ along ℓ.

Locations

• Duke Mathematical Journal - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View