COMPUTATION OF RELATIVE CLASS-NUMBERS OF CM-FIELDS

It was were known that it is easy to compute relative class numbers of abelian Chi-fields by using generalized Bernoulli numbers (see Theore m 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a t echnique for computing the relative class number of any Chi-field.