Normal integral bases of Lehmer's cyclic quintic fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911836640641024 |
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| author | Hashimoto, Yu Aoki, Miho |
| author_facet | Hashimoto, Yu Aoki, Miho |
| contents | Let $K_n$ be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric polynomial. We give all normal integral bases for $K_n$ only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that $n^4+5n^3+15n^2+25n+25$ is prime number, and Spearman-Willliams in the case that $n^4+5n^3+15n^2+25n+25$ is square-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10858 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Normal integral bases of Lehmer's cyclic quintic fields Hashimoto, Yu Aoki, Miho Number Theory Primary 11R04, 11R20, Secondary 11C08, 11L05, 11R80 Let $K_n$ be a tamely ramified cyclic quintic field generated by a root of Emma Lehmer's parametric polynomial. We give all normal integral bases for $K_n$ only by the roots of the polynomial, which is a generalization of the work of Lehmer in the case that $n^4+5n^3+15n^2+25n+25$ is prime number, and Spearman-Willliams in the case that $n^4+5n^3+15n^2+25n+25$ is square-free. |
| title | Normal integral bases of Lehmer's cyclic quintic fields |
| topic | Number Theory Primary 11R04, 11R20, Secondary 11C08, 11L05, 11R80 |
| url | https://arxiv.org/abs/2209.10858 |