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

Abstract

Let p ≡ 1 (mod 8) and q ≡ 3 (mod 8) be two prime integers and let l 6∈ {−1, p, q} be a positive odd square-free integer. Assuming that the fundamental unit of Q (√ 2p ) has a negative norm, we investigate the unit group of the fields Q (√ 2, √ p, √ q, √ −l ) .