2024/11/05 by Yulin Gong, Gong, Yulin
Computer Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2411.02929
openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the spectral distribution of damped waves on compact Anosov manifolds. Sjöstrand \citeSJ1 proved that the imaginary parts of the majority of the eigenvalues concentrate near the average of the damping function, see also Anantharaman \citeAN2. In this paper, we prove that the most of eigenvalues actually lie in certain regions with imaginary parts that approach the average logarithmically as the real parts tend to infinity. The proof relies on the moderate deviation principles for Anosov geodesic flows. As an application, we show the concentration of non-trivial zeros of twisted Selberg zeta functions in a logarithmic region asymptotically close to \Re s=(1)/(2).