On the Proportion of Coprime Fractions in Number Fields
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916178924929024 |
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| author | Bridges, Walter Franke, Johann Stumpenhusen, Johann Christian |
| author_facet | Bridges, Walter Franke, Johann Stumpenhusen, Johann Christian |
| contents | In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fraction as soon as it ``appears'' for the first time and no later. The natural density of coprime fractions in the set of reduced fractions may then be computed using well-known facts about Hecke $L$-functions. Furthermore, we draw some connections to the modular group and Heegner points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01346 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Proportion of Coprime Fractions in Number Fields Bridges, Walter Franke, Johann Stumpenhusen, Johann Christian Number Theory 11R45 In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fraction as soon as it ``appears'' for the first time and no later. The natural density of coprime fractions in the set of reduced fractions may then be computed using well-known facts about Hecke $L$-functions. Furthermore, we draw some connections to the modular group and Heegner points. |
| title | On the Proportion of Coprime Fractions in Number Fields |
| topic | Number Theory 11R45 |
| url | https://arxiv.org/abs/2311.01346 |