The Density of Borromean Primes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929353313484800 |
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| author | Ishida, Yuki Kuramoto, Atsuki Zheng, Dingchuan |
| author_facet | Ishida, Yuki Kuramoto, Atsuki Zheng, Dingchuan |
| contents | In this paper, we study an asymptotic distribution of sets of primes satisfying certain "linking conditions" in arithmetic topology, namely, conditions given by the Legendre and Rédei symbols among sets of primes. As our Main Theorem, we prove an asymptotic density formula for Borromean primes among all primes. For the proof, we use the effective Chebotarev density formula under the Generalized Riemann Hypothesis and explicit computations of discriminants of the number fields involved in Rédei's extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Density of Borromean Primes Ishida, Yuki Kuramoto, Atsuki Zheng, Dingchuan Number Theory 11R44, 11N45 In this paper, we study an asymptotic distribution of sets of primes satisfying certain "linking conditions" in arithmetic topology, namely, conditions given by the Legendre and Rédei symbols among sets of primes. As our Main Theorem, we prove an asymptotic density formula for Borromean primes among all primes. For the proof, we use the effective Chebotarev density formula under the Generalized Riemann Hypothesis and explicit computations of discriminants of the number fields involved in Rédei's extension. |
| title | The Density of Borromean Primes |
| topic | Number Theory 11R44, 11N45 |
| url | https://arxiv.org/abs/2403.17957 |