Units in Quadratic and Multi-Quadratic Fields

Adam Pratt, Maria Stadnik, Mary-Stewart Wachter

Abstract


In this paper, we investigate multi-quadratic fields, looking for those that contain units of norm \(-1\). We provide results concerning the existence of units of norm \(-1\) in fields of the form \(\mathbb{Q}(\sqrt{2p})\) for prime \(p \equiv 1 \mod 4\) and prove that all of the fields \(\mathbb{Q}(\sqrt{2},\sqrt{p})\) with \(p \equiv 5 \mod 8\) prime contain a unit of norm \(-1\).

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References


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