Quadratic extensions of the rational field, the Gauss field or the field of cubic roots of unity of caliber 1 (Q753857)

The author characterizes certain imaginary and real quadratic fields \(K\) of caliber 1. The caliber is just \(\sum^{h}_{i=1}t_ i\) where \(h\) is the class number of the field \(K\) and \(t_ i\) is the number of equivalent (district) reduced ideals in the \(i\)-th class of \(C_ K\) (the class group of \(K\)). He also addresses such questions for certain biquadratic extensions. The author leaves open such questions for cubic fields at the end of the paper.