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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.08121 |
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Table of Contents:
- In a 2008 paper Ellenberg suggested a strategy to improve the known upper bounds for the $\ell$-torsion part of class groups of number fields of fixed degree $d$. Motivated by this he proposed a question about the number of primitive elements of small height in a number field. Here we answer Ellenberg's question. We also improve Heath-Brown's bound for the $\ell$-torsion part of class groups of purely cubic number fields, and we generalize our improvement to pure fields of arbitrary odd degree $d$.