On multiplicities in length spectra of semi-arithmetic hyperbolic surfaces

2025/06/30 by Mikhail Belolipetsky, Gregory Cosac, Belolipetsky, Mikhail +5 · 1 citation
Mathematics · Physics and Astronomy · #11F06 #20H10 #58J50 #81Q50 #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Number Theory (math.NT) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2507.00211

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that semi-arithmetic surfaces of arithmetic dimension two which admit a modular embedding have exponential growth of mean multiplicities in their length spectrum. Prior to this work large mean multiplicities were rigorously confirmed only for the length spectra of arithmetic surfaces. We also discuss the relation of the degeneracies in the length spectrum and quantization of the Hamiltonian mechanical system on the surface.

Citations

• On the arithmetic dimension of triangle groups

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