Salem numbers and commensurability classes of arithmetic hyperbolic manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908816541483008 |
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| author | Chu, Michelle Murillo, Plinio G. P. |
| author_facet | Chu, Michelle Murillo, Plinio G. P. |
| contents | In this article we show that given a Salem number $λ$, a totally real number field $k\subseteq\mathbb{Q}(λ+λ^{-1})$, and a positive integer $n\geq\mathrm{deg}_k(λ)-1$, there exist infinitely many commensurability classes of arithmetic hyperbolic $n$-manifolds defined over $k$ which contain a geodesic of length $\logλ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Salem numbers and commensurability classes of arithmetic hyperbolic manifolds Chu, Michelle Murillo, Plinio G. P. Geometric Topology Number Theory In this article we show that given a Salem number $λ$, a totally real number field $k\subseteq\mathbb{Q}(λ+λ^{-1})$, and a positive integer $n\geq\mathrm{deg}_k(λ)-1$, there exist infinitely many commensurability classes of arithmetic hyperbolic $n$-manifolds defined over $k$ which contain a geodesic of length $\logλ$. |
| title | Salem numbers and commensurability classes of arithmetic hyperbolic manifolds |
| topic | Geometric Topology Number Theory |
| url | https://arxiv.org/abs/2506.20552 |