An $Ω$-Result for the Counting of Geodesic Segments in the Hyperbolic Plane
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912632825446400 |
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| author | Voskou, Marios |
| author_facet | Voskou, Marios |
| contents | Let $Γ$ be a cocompact Fuchsian group, and $l$ a fixed closed geodesic. We study the counting of those images of $l$ that have a distance from $l$ less than or equal to $R$. We prove an $Ω$-result for the error term in the asymptotic expansion of the counting function. More specifically, we prove that the error term is equal to $Ω_δ\left(X^{1/2}\left(\log{\log{X}}\right)^{1/4-δ} \right)$, where $X=\cosh{R}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An $Ω$-Result for the Counting of Geodesic Segments in the Hyperbolic Plane Voskou, Marios Number Theory Primary 11F72, Secondary 11L07 Let $Γ$ be a cocompact Fuchsian group, and $l$ a fixed closed geodesic. We study the counting of those images of $l$ that have a distance from $l$ less than or equal to $R$. We prove an $Ω$-result for the error term in the asymptotic expansion of the counting function. More specifically, we prove that the error term is equal to $Ω_δ\left(X^{1/2}\left(\log{\log{X}}\right)^{1/4-δ} \right)$, where $X=\cosh{R}$. |
| title | An $Ω$-Result for the Counting of Geodesic Segments in the Hyperbolic Plane |
| topic | Number Theory Primary 11F72, Secondary 11L07 |
| url | https://arxiv.org/abs/2411.12567 |