An asymptotic on the logarithms of the relative class numbers of imaginary abelian number fields of prime conductor and large degree
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916591971598336 |
|---|---|
| author | Louboutin, Stéphane |
| author_facet | Louboutin, Stéphane |
| contents | An asymptotic on the logarithms of the relative class numbers of the cyclotomic number fields of prime conductors $p$ is known. Here we give an asymptotic on the logarithms of the relative class numbers of the imaginary abelian number fields of prime conductors $p$ and large degrees $m =(p-1)/d$ with $ϕ(d)=o(\log p)$. We also show that this asymptotic does not hold true anymore under the only slightly weaker restriction $ϕ(d)=O(\log p)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An asymptotic on the logarithms of the relative class numbers of imaginary abelian number fields of prime conductor and large degree Louboutin, Stéphane Number Theory 11R20, 11R29, 11R42 An asymptotic on the logarithms of the relative class numbers of the cyclotomic number fields of prime conductors $p$ is known. Here we give an asymptotic on the logarithms of the relative class numbers of the imaginary abelian number fields of prime conductors $p$ and large degrees $m =(p-1)/d$ with $ϕ(d)=o(\log p)$. We also show that this asymptotic does not hold true anymore under the only slightly weaker restriction $ϕ(d)=O(\log p)$. |
| title | An asymptotic on the logarithms of the relative class numbers of imaginary abelian number fields of prime conductor and large degree |
| topic | Number Theory 11R20, 11R29, 11R42 |
| url | https://arxiv.org/abs/2501.18941 |