Fractal Uncertainty for Transfer Operators
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Author(s)
Dyatlov, Semen
Zworski, Maciej
Date Issued
March 2018
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Dyatlov, Semen & Maciej Zworski. "Fractal Uncertainty for Transfer Operators." International Mathematics Research Notices (March 2018): rny026 © 2018 The Authors
Version
Author's final manuscript
Abstract
We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there exists σ > 0 for which the Selberg zeta function (1.2) for a convex co-compact hyperbolic surface has only finitely many zeros with Re s≥1/2−σ. That eliminates advanced microlocal techniques of Dyatlov–Zahl [6], though we stress that these techniques are still needed for resolvent bounds and for possible generalizations to the case of nonconstant curvature.
Subjects
General Mathematics
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/imrn/rny026
