On the 4-rank of class groups of Dirichlet biquadratic fields

Fouvry, Étienne; Koymans, Peter; Pagano, Carlo

doi:10.1017/S1474748020000651

アイテム詳細

登録内容を編集ファイル形式で保存

一時保存へ追加

タグ情報を表示リリース履歴を表示詳細要約

公開

学術論文

On the 4-rank of class groups of Dirichlet biquadratic fields

MPS-Authors

/persons/resource/persons262194

Koymans, Peter
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons248540

Pagano, Carlo
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1017/S1474748020000651
(出版社版)

https://doi.org/10.48550/arXiv.2003.11406
(プレプリント)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

フルテキスト (公開)

公開されているフルテキストはありません

付随資料 (公開)

There is no public supplementary material available

引用

Fouvry, É., Koymans, P., & Pagano, C. (2022). On the 4-rank of class groups of Dirichlet biquadratic fields. Journal of the Institute of Mathematics of Jussieu, 21(5), 1543-1570. doi:10.1017/S1474748020000651.

引用: https://hdl.handle.net/21.11116/0000-0008-AF65-2

要旨

We show that for 100\% of the odd, squarefree integers $n > 0$ the $4$-rank
of $\text{Cl}(\mathbb{Q}(i, \sqrt{n}))$ is equal to $\omega_3(n) - 1$, where
$\omega_3$ is the number of prime divisors of $n$ that are $3$ modulo $4$.