Spectral gaps without the pressure condition
Name
1612.09040.pdf
Description
Submitted version
Size
698.08 KB
Format
Adobe PDF
Checksum (MD5)
b8de72bd8217f286c9f977b19c90abf7
Author(s)
Bourgain, Jean
Dyatlov, Semyon
Date Issued
May 2018
Journal
Annals of Mathematics
Publisher
Mathematics Department, Princeton University
Citation
Bourgain, Jean and Semyon Dyatlov. "Spectral gaps without the pressure condition." Annals of Mathematics 187, 3 (May 2018): 825-867 © 2018 Department of Mathematics, Princeton University
Version
Original manuscript
Abstract
For all convex co-compact hyperbolic surfaces, we prove the existence of an essential spectral gap, that is, a strip beyond the unitarity axis in which the Selberg zeta function has only finitely many zeroes. We make no assumption on the dimension δ of the limit set; in particular, we do not require the pressure condition δ ≤ 1/2 . This is the first result of this kind for quantum Hamiltonians. Our proof follows the strategy developed by Dyatlov and Zahl. The main new ingredient is the fractal uncertainty principle for δ-regular sets with δ < 1, which may be of independent interest.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4007/ANNALS.2018.187.3.5
