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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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Table of 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.