A Central Limit Theorem for the Winding Number of Low-Lying Closed Geodesics
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911730043453440 |
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| author | Dubno, Elias |
| author_facet | Dubno, Elias |
| contents | We show that the winding of low-lying closed geodesics on the modular surface has a Gaussian limiting distribution when normalized by any standard notion of length, in contrast to the Cauchy distribution arising when allowing arbitrarily deep excursions into the cusp. In addition, we prove a Berry-Esseen bound and a local limit theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Central Limit Theorem for the Winding Number of Low-Lying Closed Geodesics Dubno, Elias Number Theory Dynamical Systems We show that the winding of low-lying closed geodesics on the modular surface has a Gaussian limiting distribution when normalized by any standard notion of length, in contrast to the Cauchy distribution arising when allowing arbitrarily deep excursions into the cusp. In addition, we prove a Berry-Esseen bound and a local limit theorem. |
| title | A Central Limit Theorem for the Winding Number of Low-Lying Closed Geodesics |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2507.23706 |