On the $2$-torsion in class groups of number fields
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914189893697536 |
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| author | Bonolis, Dante |
| author_facet | Bonolis, Dante |
| contents | In $2020$, Bhargava, Shankar, Taniguchi, Thorne, Tsimerman, and Zhao proved that for a finite extension $K/\mathbb{Q}$ of degree $n\geq 5$, the size of the $2$-torsion class group is bounded by $\# h_{2}(K)=O_{n,\varepsilon}(D_{K}^{\frac{1}{2}-\frac{1}{2n}+\varepsilon})$, where $D_{K}$ is the absolute discriminant of $K$. In the present paper, we improve their bound by proving that $\# h_{2}(K)=O_{n,\varepsilon}(D_{K}^{\frac{1}{2}-\frac{1}{2n}-δ_{K}+\varepsilon})$, for a constant $δ_{K}\geq\frac{1}{28n}-\frac{3}{28n(n-1)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $2$-torsion in class groups of number fields Bonolis, Dante Number Theory In $2020$, Bhargava, Shankar, Taniguchi, Thorne, Tsimerman, and Zhao proved that for a finite extension $K/\mathbb{Q}$ of degree $n\geq 5$, the size of the $2$-torsion class group is bounded by $\# h_{2}(K)=O_{n,\varepsilon}(D_{K}^{\frac{1}{2}-\frac{1}{2n}+\varepsilon})$, where $D_{K}$ is the absolute discriminant of $K$. In the present paper, we improve their bound by proving that $\# h_{2}(K)=O_{n,\varepsilon}(D_{K}^{\frac{1}{2}-\frac{1}{2n}-δ_{K}+\varepsilon})$, for a constant $δ_{K}\geq\frac{1}{28n}-\frac{3}{28n(n-1)}$. |
| title | On the $2$-torsion in class groups of number fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.21899 |