On the height of some generators of galois extensions with big galois group
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915023767470080 |
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| author | Jenvrin, Jonathan |
| author_facet | Jenvrin, Jonathan |
| contents | We study the height of generators of Galois extensions of the rationals having the alternating group $\mathfrak{A}_n$ as Galois group. We prove that if such generators are obtained from certain, albeit classical, constructions, their height tends to infinity as $n$ increases. This provides an analogue of a result by Amoroso, originally established for the symmetric group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the height of some generators of galois extensions with big galois group Jenvrin, Jonathan Number Theory 11G50, 11R32 We study the height of generators of Galois extensions of the rationals having the alternating group $\mathfrak{A}_n$ as Galois group. We prove that if such generators are obtained from certain, albeit classical, constructions, their height tends to infinity as $n$ increases. This provides an analogue of a result by Amoroso, originally established for the symmetric group. |
| title | On the height of some generators of galois extensions with big galois group |
| topic | Number Theory 11G50, 11R32 |
| url | https://arxiv.org/abs/2403.00500 |