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1 November 2010 Large values of eigenfunctions on arithmetic hyperbolic surfaces
Djordje Milićević
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Duke Math. J. 155(2): 365-401 (1 November 2010). DOI: 10.1215/00127094-2010-058

Abstract

We prove a new omega result for extreme values of high-energy Hecke-Maass eigenforms on arithmetic hyperbolic surfaces. In particular we show that they exhibit much stronger fluctuations in the L-aspect than what the random wave conjecture would have predicted. We adapt the method of resonators and connect values of eigenfunctions to global geometry of these surfaces by employing the pre-trace formula and twists by Hecke correspondences.

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Djordje Milićević. "Large values of eigenfunctions on arithmetic hyperbolic surfaces." Duke Math. J. 155 (2) 365 - 401, 1 November 2010. https://doi.org/10.1215/00127094-2010-058

Information

Published: 1 November 2010
First available in Project Euclid: 27 October 2010

zbMATH: 1219.11071
MathSciNet: MR2736169
Digital Object Identifier: 10.1215/00127094-2010-058

Subjects:
Primary: 11F37
Secondary: 11F32, 11N56, 58J50, 81Q50

Rights: Copyright © 2010 Duke University Press

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Vol.155 • No. 2 • 1 November 2010
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