Geodesic restrictions of arithmetic eigenfunctions

Abstract

Let X be an arithmetic hyperbolic surface, ψa Hecke-Maass form, and l a geodesic segment on X. We obtain a power saving over the local bound of Burq-Gérard-Tzvetkov for the L^2 norm of ψrestricted 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 ψalong l.

35 pages

References in corpus (6)

• Distribution of mass of holomorphic cusp forms
• Nodal domains of Maass forms I
• Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions
• Subconvexity for sup-norms of automorphic forms on PGL(n)
• Nodal domains of Maass forms II
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Cited by in corpus (7)

• Quantum ergodicity and $L^p$ norms of restrictions of eigenfunctions
• Equidistribution of Eisenstein series on geodesic segments
• Geodesic bi-angles and Fourier coefficients of restrictions of eigenfunctions
• Bounds of restriction of characters to submanifolds
• Restrictions of SL_3 Maass forms to maximal flat subspaces
• Extreme values of geodesic periods on arithmetic hyperbolic surfaces
• $L^p$-Norm Bounds for Automorphic Forms via Spectral Reciprocity