Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p

Franz Lemmermeyer

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arXiv · 2510.10295

Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p

Franz Lemmermeyer

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Abstract

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.

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Franz Lemmermeyer. 2025-10-11. Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p. https://arxiv.org/abs/2510.10295

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