Erdős-Kac type theorem for the number of scattering geodesics on modular surface
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909643124506624 |
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| author | Pujahari, Sudhir Satpathy, Punya Plaban |
| author_facet | Pujahari, Sudhir Satpathy, Punya Plaban |
| contents | In 1917, Hardy and Ramanujan showed that if $ω(n)$ is the number of distinct prime factors of a randomly chosen positive integer $n,$ then the normal order of $ω(n)$ is $\log \log \, n.$ This led Erdős and Kac to prove their celebrated result showing a Gaussian behaviour for $ω(n).$ In this article we prove an Erdős-Kac kind result for the number of scattering geodesics on the modular surface with a common sojourn time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Erdős-Kac type theorem for the number of scattering geodesics on modular surface Pujahari, Sudhir Satpathy, Punya Plaban Number Theory Differential Geometry In 1917, Hardy and Ramanujan showed that if $ω(n)$ is the number of distinct prime factors of a randomly chosen positive integer $n,$ then the normal order of $ω(n)$ is $\log \log \, n.$ This led Erdős and Kac to prove their celebrated result showing a Gaussian behaviour for $ω(n).$ In this article we prove an Erdős-Kac kind result for the number of scattering geodesics on the modular surface with a common sojourn time. |
| title | Erdős-Kac type theorem for the number of scattering geodesics on modular surface |
| topic | Number Theory Differential Geometry |
| url | https://arxiv.org/abs/2506.07474 |