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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.00611 |
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| _version_ | 1866910924831457280 |
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| author | Chan, Stephanie Koymans, Peter |
| author_facet | Chan, Stephanie Koymans, Peter |
| contents | Ellenberg--Venkatesh proved in 2007 that $h_3(d) \ll_ε|d|^{1/3 + ε}$, where $h_3(d)$ denotes the size of the $3$-torsion of the class group of $\mathbb{Q}(\sqrt{d})$. We improve this bound to $h_3(d) \ll_ε|d|^{κ+ ε}$ with $κ\approx 0.3193 \cdots$. We also combine our methods with work of Heath-Brown--Pierce to give new bounds for average $\ell$-torsion of real quadratic fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new pointwise bound for $3$-torsion of class groups Chan, Stephanie Koymans, Peter Number Theory Ellenberg--Venkatesh proved in 2007 that $h_3(d) \ll_ε|d|^{1/3 + ε}$, where $h_3(d)$ denotes the size of the $3$-torsion of the class group of $\mathbb{Q}(\sqrt{d})$. We improve this bound to $h_3(d) \ll_ε|d|^{κ+ ε}$ with $κ\approx 0.3193 \cdots$. We also combine our methods with work of Heath-Brown--Pierce to give new bounds for average $\ell$-torsion of real quadratic fields. |
| title | A new pointwise bound for $3$-torsion of class groups |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.00611 |