Large values of eigenfunctions on arithmetic hyperbolic surfaces
Djordje Milićević
Source: Duke Math. J. Volume 155, Number 2
(2010), 365-401.
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 $L^{\infty}$-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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1288185459
Digital Object Identifier: doi:10.1215/00127094-2010-058
Mathematical Reviews number (MathSciNet): MR2736169
Zentralblatt MATH identifier: 1219.11071
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