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15 February 2016 Geodesic restrictions of arithmetic eigenfunctions
Simon Marshall
Duke Math. J. 165(3): 463-508 (15 February 2016). DOI: 10.1215/00127094-3166736

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 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 .

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Simon Marshall. "Geodesic restrictions of arithmetic eigenfunctions." Duke Math. J. 165 (3) 463 - 508, 15 February 2016. https://doi.org/10.1215/00127094-3166736

Information

Received: 16 July 2013; Revised: 11 March 2015; Published: 15 February 2016
First available in Project Euclid: 10 December 2015

zbMATH: 1377.11059
MathSciNet: MR3466161
Digital Object Identifier: 10.1215/00127094-3166736

Subjects:
Primary: 35P20
Secondary: 11F25, 11F41

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 3 • 15 February 2016
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