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arXiv · 1710.05430

Fractal uncertainty for transfer operators

Semyon Dyatlov·Maciej Zworski
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Abstract

We show directly that the fractal uncertainty principle of Bourgain-Dyatlov [arXiv:1612.09040] implies that there exists $ σ> 0 $ for which the Selberg zeta function for a convex co-compact hyperbolic surface has only finitely many zeros with $ \Re s \geq \frac12 - σ$. That eliminates advanced microlocal techniques of Dyatlov-Zahl [arXiv:1504.06589] though we stress that these techniques are still needed for resolvent bounds and for possible generalizations to the case of non-constant curvature.

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Semyon Dyatlov, Maciej Zworski. 2018-02-02. Fractal uncertainty for transfer operators. https://doi.org/10.1093/imrn%2Frny026

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