Spectral gaps without the pressure condition
Author(s)
Bourgain, Jean; Dyatlov, Semyon
DownloadSubmitted version (698.0Kb)
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2018-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
0003-486X