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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.10136 |
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| _version_ | 1866917612215074816 |
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| author | Koymans, Peter Rome, Nick |
| author_facet | Koymans, Peter Rome, Nick |
| contents | Let $A$ be a finite, abelian group. We show that the density of $A$-extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This strengthens earlier work of Frei--Loughran--Newton \cite{FLN}, who obtained a density result under the additional assumption that $A/A[\ell]$ is cyclic with $\ell$ denoting the smallest prime divisor of $\# A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10136 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on the Hasse norm principle Koymans, Peter Rome, Nick Number Theory 11R45, 14G12 Let $A$ be a finite, abelian group. We show that the density of $A$-extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This strengthens earlier work of Frei--Loughran--Newton \cite{FLN}, who obtained a density result under the additional assumption that $A/A[\ell]$ is cyclic with $\ell$ denoting the smallest prime divisor of $\# A$. |
| title | A note on the Hasse norm principle |
| topic | Number Theory 11R45, 14G12 |
| url | https://arxiv.org/abs/2301.10136 |