On units of some fields of the form $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l}\big)$

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}\big(\sqrt{2p}\big) $ has a negative norm, we investigate the unit group of the fields $\mathbb{Q}\big(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell} \big)$.

Keywords

• multiquadratic number field
• unit group
• fundamental system of units