Duke Mathematical Journal

Geodesic restrictions of arithmetic eigenfunctions

Simon Marshall

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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 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 , 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 .

Article information

Duke Math. J., Volume 165, Number 3 (2016), 463-508.

Received: 16 July 2013
Revised: 11 March 2015
First available in Project Euclid: 10 December 2015

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Zentralblatt MATH identifier

Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions
Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable) 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]

Maass form amplification symptotics of eigenfunctions


Marshall, Simon. Geodesic restrictions of arithmetic eigenfunctions. Duke Math. J. 165 (2016), no. 3, 463--508. doi:10.1215/00127094-3166736. https://projecteuclid.org/euclid.dmj/1449771973

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