Mathematica Bohemica, Vol. 148, No. 2, pp. 237-242, 2023
On units of some fields of the form $\mathbb{Q}(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell})$
Mohamed Mahmoud Chems-Eddin
Received August 25, 2021. Published online June 7, 2022.
Abstract: Let $p\equiv1\pmod8$ and $q\equiv3\pmod8$ be two prime integers and let $\ell\not\in\{-1, p, q\}$ be a positive odd square-free integer. Assuming that the fundamental unit of $\mathbb{Q}(\sqrt{2p}) $ has a negative norm, we investigate the unit group of the fields $\mathbb{Q}(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell} )$.
Keywords: multiquadratic number field; unit group; fundamental system of units
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Affiliations: Mohamed Mahmoud Chems-Eddin, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Fez, Morocco e-mail: 2m.chemseddin@gmail.com
