On Multiplicities in Length Spectra of Semi-Arithmetic Hyperbolic Surfaces
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.
Authors
- Cayo Dória (ORCID: https://orcid.org/0000-0003-2654-8915)
- Gisele Teixeira Paula (ORCID: https://orcid.org/0000-0002-0877-4831)
- Gregory Cosac (ORCID: https://orcid.org/0000-0002-5033-9892)
- Mikhail Belolipetsky (ORCID: https://orcid.org/0000-0003-2709-4775)
Institutions
- Instituto Nacional de Matemática Pura e Aplicada (BR)
- Brazilian Society of Computational and Applied Mathematics (BR)
- Fundação Carlos Chagas (BR)
- Universidade Federal do Paraná (BR)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2026-03-09
- DOI
- https://doi.org/10.1007/s00220-026-05581-w
- Primary Topic
- Geometric and Algebraic Topology
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Centre National de la Recherche Scientifique
- Institut Henri Poincaré
- Sorbonne Université