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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2505.00484 |
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| _version_ | 1866916716009750528 |
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| author | Kim, Daejun Lee, Seok Hyeong Lee, Seungjai |
| author_facet | Kim, Daejun Lee, Seok Hyeong Lee, Seungjai |
| contents | In this paper, we study the Dirichlet series that enumerates proper equivalence classes of full-rank sublattices of a given quadratic lattice in a hyperbolic plane -- that is, a nondegenerate isotropic quadratic space of dimension $2$. We derive explicit formulas for the associated zeta functions and obtain a combinatorial way to compute them. Their analytic properties lead to the intriguing consequence that a large proportion of proper classes are one-lattice classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zeta functions of quadratic lattices of a hyperbolic plane Kim, Daejun Lee, Seok Hyeong Lee, Seungjai Number Theory In this paper, we study the Dirichlet series that enumerates proper equivalence classes of full-rank sublattices of a given quadratic lattice in a hyperbolic plane -- that is, a nondegenerate isotropic quadratic space of dimension $2$. We derive explicit formulas for the associated zeta functions and obtain a combinatorial way to compute them. Their analytic properties lead to the intriguing consequence that a large proportion of proper classes are one-lattice classes. |
| title | Zeta functions of quadratic lattices of a hyperbolic plane |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.00484 |