Irrationality of the Length Spectrum
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912297271689216 |
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| author | Peterzil, George Sapire, Guy |
| author_facet | Peterzil, George Sapire, Guy |
| contents | It is a classical result of Dal'Bo that the length spectrum of a non-elementary Fuchsian group is non-arithmetic, namely, it generates a dense additive subgroup of $\mathbb{R}$. In this note we provide an elementary proof of an extension of this theorem: a non-elementary Fuchsian group contains two elements whose lengths are linearly independent over $\mathbb{Q}$, reproving a result of Prasad and Rapinchuk. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irrationality of the Length Spectrum Peterzil, George Sapire, Guy Geometric Topology Dynamical Systems 20H10 (Primary) 37D40 (Secondary) It is a classical result of Dal'Bo that the length spectrum of a non-elementary Fuchsian group is non-arithmetic, namely, it generates a dense additive subgroup of $\mathbb{R}$. In this note we provide an elementary proof of an extension of this theorem: a non-elementary Fuchsian group contains two elements whose lengths are linearly independent over $\mathbb{Q}$, reproving a result of Prasad and Rapinchuk. |
| title | Irrationality of the Length Spectrum |
| topic | Geometric Topology Dynamical Systems 20H10 (Primary) 37D40 (Secondary) |
| url | https://arxiv.org/abs/2503.03461 |