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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2402.04908 |
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| _version_ | 1866916484173791232 |
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| author | Jenvrin, Jonathan |
| author_facet | Jenvrin, Jonathan |
| contents | Amoroso and Masser proved that for every real $ε> 0$, there exists a constant $c(ε)>0$, such that for every algebraic number $α$ with $\mathbb{Q}(α)/\mathbb{Q}$ being a Galois extension, the height of $α$ is either 0 or at least $c(ε) [\mathbb{Q}(α):\mathbb{Q}]^{-ε}$. In this article we establish an explicit version of this theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Explicit lower bounds for the height in Galois extensions of number fields Jenvrin, Jonathan Number Theory 11G50 Amoroso and Masser proved that for every real $ε> 0$, there exists a constant $c(ε)>0$, such that for every algebraic number $α$ with $\mathbb{Q}(α)/\mathbb{Q}$ being a Galois extension, the height of $α$ is either 0 or at least $c(ε) [\mathbb{Q}(α):\mathbb{Q}]^{-ε}$. In this article we establish an explicit version of this theorem. |
| title | Explicit lower bounds for the height in Galois extensions of number fields |
| topic | Number Theory 11G50 |
| url | https://arxiv.org/abs/2402.04908 |