Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908587697111040 |
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| author | Lemmermeyer, Franz |
| author_facet | Lemmermeyer, Franz |
| contents | In this article we explain how to construct cyclic octic unramfied extensions of the real quadratic number field $k = {\mathbb Q}(\sqrt{2p}\,)$, where $p \equiv 1 \bmod 8$ is a prime number such that $h_2(k) \equiv 0 \bmod 8$. The construction only requires solving the diophantine equation $eu^2 = t^2 + 2ps^2$ in integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p Lemmermeyer, Franz Number Theory 11R37 In this article we explain how to construct cyclic octic unramfied extensions of the real quadratic number field $k = {\mathbb Q}(\sqrt{2p}\,)$, where $p \equiv 1 \bmod 8$ is a prime number such that $h_2(k) \equiv 0 \bmod 8$. The construction only requires solving the diophantine equation $eu^2 = t^2 + 2ps^2$ in integers. |
| title | Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p |
| topic | Number Theory 11R37 |
| url | https://arxiv.org/abs/2510.10295 |