The class number one problem for some totally complex quartic number fields
Let \(K\) be a totally complex quartic field whose class number is equal to \(1\). The authors prove that there are 95 non-isomorphic fields \(K\) whose rings of algebraic integers are generated by an algebraic unit. Moreover, they prove Louboutin's conjecture according to which a totally complex quartic unit \(\varepsilon\) generally generates the unit group of the quartic order \(\mathbb Z[\varepsilon]\).
scientific article; zbMATH DE number 5559083