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arXiv · 2105.11350

The construction of the Hilbert genus fields of real cyclic quartic fields

Mohamed Mahmoud Chems-Eddin·Moulay Ahmed Hajjami·Mohammed Taous
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Abstract

Let $p$ be a prime number such that $p=2$ or $p\equiv 1\pmod 4$. Let $\varepsilon_p$ denote the fundamental unit of $\mathbb{Q}(\sqrt{p})$ and let $a$ be a positive square-free integer. In the present paper, we construct the Hilbert genus field of the real cyclic quartic fields $\mathbb{Q}(\sqrt{a\varepsilon_p\sqrt{p}})$.

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Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous. 2021-05-24. The construction of the Hilbert genus fields of real cyclic quartic fields. https://doi.org/10.7169/facm%2F2014

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