The hyperbolic lattice counting problem in large dimensions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866915354646675456 |
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| author | Katsivelos, Christos |
| author_facet | Katsivelos, Christos |
| contents | For $n\geq 3$ and $Γ$ a cocompact lattice acting on the hyperbolic space $\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $Γ\backslash\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $Ω$-results for the mean value and the second moment of the error term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17753 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The hyperbolic lattice counting problem in large dimensions Katsivelos, Christos Number Theory Primary 11F72, Secondary 37C35, 37D40 For $n\geq 3$ and $Γ$ a cocompact lattice acting on the hyperbolic space $\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $Γ\backslash\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $Ω$-results for the mean value and the second moment of the error term. |
| title | The hyperbolic lattice counting problem in large dimensions |
| topic | Number Theory Primary 11F72, Secondary 37C35, 37D40 |
| url | https://arxiv.org/abs/2506.17753 |