Duke Mathematical Journal

Geodesic restrictions of arithmetic eigenfunctions

Simon Marshall

Abstract

Let $X$ be an arithmetic hyperbolic surface arising from a quaternion division algebra over $\mathbb{Q}$. Let $\psi$ be a Hecke–Maass form on $X$, and let $\ell$ be a geodesic segment. We obtain a power saving over the local bound of Burq, Gérard, and Tzvetkov for the $L^{2}$-norm of $\psi$ restricted to $\ell$, by extending the technique of arithmetic amplification developed by Iwaniec and Sarnak. We also improve the local bounds for various Fourier coefficients of $\psi$ along $\ell$.

Article information

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

Dates
Revised: 11 March 2015
First available in Project Euclid: 10 December 2015

https://projecteuclid.org/euclid.dmj/1449771973

Digital Object Identifier
doi:10.1215/00127094-3166736

Mathematical Reviews number (MathSciNet)
MR3466161

Zentralblatt MATH identifier
1377.11059

Citation

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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