On multiplicities in length spectra of semi-arithmetic hyperbolic surfaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912889254707200 |
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| author | Belolipetsky, Mikhail Cosac, Gregory Dória, Cayo Paula, Gisele Teixeira |
| author_facet | Belolipetsky, Mikhail Cosac, Gregory Dória, Cayo Paula, Gisele Teixeira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On multiplicities in length spectra of semi-arithmetic hyperbolic surfaces Belolipetsky, Mikhail Cosac, Gregory Dória, Cayo Paula, Gisele Teixeira Group Theory Mathematical Physics Number Theory 20H10, 11F06, 58J50, 81Q50 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. |
| title | On multiplicities in length spectra of semi-arithmetic hyperbolic surfaces |
| topic | Group Theory Mathematical Physics Number Theory 20H10, 11F06, 58J50, 81Q50 |
| url | https://arxiv.org/abs/2507.00211 |