PreprintarXiv licencearXiv
Escape of mass for finite-area hyperbolic surfaces
Abstract
Let M be a noncompact finite-area hyperbolic surface. We give a lower bound for the L2 norm of eigenfunctions and Eisenstein series in a compact part of the surface. This extends a result of Soundararajan [arXiv:0901.4060] to the nonarithmetic setting. The crucial components of the proof are a long-time Egorov's theorem designed for this setting, a nonlinear uncertainty principle of Cohen--Dyatlov [arXiv:2609.30261], and an application of Weyl's method for exponential sums.
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BibTeX
@misc{cohen2026escape,
title = {{Escape of mass for finite-area hyperbolic surfaces}},
author = {Alex Cohen and Zhenhao Li and Zhongkai Tao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37573},
eprint = {2610.37573},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37573},
}
RIS
TY - UNPB
TI - Escape of mass for finite-area hyperbolic surfaces
AU - Alex Cohen
AU - Zhenhao Li
AU - Zhongkai Tao
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37573
UR - https://arxiv.org/abs/2610.37573
AB - Let M be a noncompact finite-area hyperbolic surface. We give a lower bound for the L^2 norm of eigenfunctions and Eisenstein series in a compact part of the surface. This extends a result of Soundararajan [arXiv:0901.4060] to the nonarithmetic setting. The crucial components of the proof are a long-time Egorov's theorem designed for this setting, a nonlinear uncertainty principle of Cohen--Dyatlov [arXiv:2609.30261], and an application of Weyl's method for exponential sums.
ER -