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Keywords:
multiquadratic number field; unit group; fundamental system of units
multiquadratic number field; unit group; fundamental system of units
Summary:
Let $p\equiv 1\pmod {8}$ and $q\equiv 3\pmod 8$ 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 $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-\ell } \big )$.
References:
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