$\ell$-Torsion in Class Groups via Dirichlet $L$-functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915091853606912 |
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| author | Heath-Brown, D. R. |
| author_facet | Heath-Brown, D. R. |
| contents | For a prime $\ell$, let $h_\ell(K)$ denote the $\ell$-part of the class number of the number field $K$. We investigate upper bounds for $h_\ell(K)$ when $K$ is quadratic or cubic, particularly in the case in which the discriminant of $K$ is smooth. This is achieved using properties of Dirichlet $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\ell$-Torsion in Class Groups via Dirichlet $L$-functions Heath-Brown, D. R. Number Theory 11R29, 11R16 For a prime $\ell$, let $h_\ell(K)$ denote the $\ell$-part of the class number of the number field $K$. We investigate upper bounds for $h_\ell(K)$ when $K$ is quadratic or cubic, particularly in the case in which the discriminant of $K$ is smooth. This is achieved using properties of Dirichlet $L$-functions. |
| title | $\ell$-Torsion in Class Groups via Dirichlet $L$-functions |
| topic | Number Theory 11R29, 11R16 |
| url | https://arxiv.org/abs/2412.07701 |