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Hasse unit indices of dihedral octic CM-fields. (English) Zbl 0972.11105
By modifying ideas of T. Kubota [Nagoya Math. J. 10, 65–85 (1956; Zbl 0074.03001)] for computing square roots of units in bicyclic quartic extensions of the rationals, the author develops a method for calculating the Hasse unit index \((E_N : W_NE^+)\) of octic dihedral CM-fields \(N\); here \(E_N\) is the unit group of \(N\), \(E^+\) is the unit group of the maximal real subfield of \(N\), and \(W_N\) is the group of roots of unity contained in \(N\). The method is illustrated by an example.

MSC:
11R27 Units and factorization
11R21 Other number fields
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