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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.10343 |
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| _version_ | 1866914870385967104 |
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| author | O'Desky, Andrew |
| author_facet | O'Desky, Andrew |
| contents | Let $K$ be a tamely ramified abelian cubic number field with discriminant $D_K$. We prove that the number of trace-one monic integral polynomials with root field $K$ and height $H$ is equal to the number of ideals in the quadratic field $\mathbb Q(\sqrt{-3})$ with norm $H^2 D_K^{-1/2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On trace-one generators of abelian cubic fields O'Desky, Andrew Number Theory 11C08, 11G50, 14M25 Let $K$ be a tamely ramified abelian cubic number field with discriminant $D_K$. We prove that the number of trace-one monic integral polynomials with root field $K$ and height $H$ is equal to the number of ideals in the quadratic field $\mathbb Q(\sqrt{-3})$ with norm $H^2 D_K^{-1/2}$. |
| title | On trace-one generators of abelian cubic fields |
| topic | Number Theory 11C08, 11G50, 14M25 |
| url | https://arxiv.org/abs/2407.10343 |