Elliptic units and genus theory (Q1076722)

The author proves results from genus theory by using analytical class number formulas and the theory of elliptic units: if K is an imaginary quadratic field and L/K a cyclic extension of prime degree \(\ell\) with d primes of K ramified in it, then \(\ell^{d-1}\) divides the quotient of class numbers \(h_ L/h_ K\) (here up to a fudge factor involving numbers of roots of unity in L and K). The author also gives results similar to \textit{H. W. Leopoldt}'s theory of ''Auflösung'' of a character [Math. Nachr. 9, 351-362 (1953; Zbl 0053.355)].