Geodesic Restrictions of Arithmetic Eigenfunctions
نویسنده
چکیده
Let X be an arithmetic hyperbolic surface arising from a quaternion division algebra over Q. Let be a Hecke–Maass form on X , and let ` be a geodesic segment. We obtain a power saving over the local bound of Burq, Gérard, and Tzvetkov for the L-norm of restricted to `, by extending the technique of arithmetic amplification developed by Iwaniec and Sarnak. We also improve the local bounds for various Fourier coefficients of along `.
منابع مشابه
ENTROPY OF GEODESIC FLOWS ON SUBSPACES OF HECKE SURFACE WITH ARITHMETIC CODE
There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...
متن کاملNorms of Geodesic Restrictions for Eigenfunctions on Hyperbolic Surfaces and Representation Theory
We consider restrictions along closed geodesics and geodesic circles for eigenfunctions of the Laplace-Beltrami operator on a compact hyperbolic Riemann surface. We obtain a non-trivial bound on the L-norm of such restrictions as the eigenvalue tends to infinity. We use methods from the theory of automorphic functions and in particular the uniqueness of invariant functionals on irreducible unit...
متن کاملEntropy of Quantum Limits
as i→∞.) A similar conjecture can be stated also in the finite volume case [6]. Of particular number theoretic interest are manifolds of the form Γ\H with Γ a congruence arithmetic lattice, in which case it is natural to assume that the eigenfunctions are Hecke-Maas forms, i.e. also eigenfunctions of all Hecke operators. We shall refer to this special case of Conjecture 1.1 as the Arithmetic Qu...
متن کاملThe length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces
We examine the relationship between the length spectrum and the geometric genus spectrum of an arithmetic hyperbolic 3-orbifold M . In particular we analyze the extent to which the geometry of M is determined by the closed geodesics coming from finite area totally geodesic surfaces. Using techniques from analytic number theory, we address the following problems: Is the commensurability class of...
متن کاملLocal and Global Analysis of Eigenfunctions on Riemannian Manifolds
This is a survey on eigenfunctions of the Laplacian on Riemannian manifolds (mainly compact and without boundary). We discuss both local results obtained by analyzing eigenfunctions on small balls, and global results obtained by wave equation methods. Among the main topics are nodal sets, quantum limits, and L norms of global eigenfunctions. The emphasis is on the connection between the behavio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016