Counting abelian number fields with restricted ramification type
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909668490608640 |
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| author | Tavernier, Julie |
| author_facet | Tavernier, Julie |
| contents | We count abelian number fields ordered by arbitrary height function whose generator of tame inertia is restricted to lie in a given subset of the Galois group, and find an explicit formula for the leading constant. We interpret our results as a version of the Batyrev-Manin conjecture on $BG$ and rephrase our result on number fields with restricted ramification type in terms of integral points on $BG$. We also prove that such number fields are equidistributed with respect to suitable collections of infinitely many local conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting abelian number fields with restricted ramification type Tavernier, Julie Number Theory We count abelian number fields ordered by arbitrary height function whose generator of tame inertia is restricted to lie in a given subset of the Galois group, and find an explicit formula for the leading constant. We interpret our results as a version of the Batyrev-Manin conjecture on $BG$ and rephrase our result on number fields with restricted ramification type in terms of integral points on $BG$. We also prove that such number fields are equidistributed with respect to suitable collections of infinitely many local conditions. |
| title | Counting abelian number fields with restricted ramification type |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.00448 |