Published online by Cambridge University Press: 24 October 2008
Let K be a quadratic imaginary number field with discriminant less than −4. For N either a number field or a finite extension of the p-adic field p, we let
N denote the ring of integers of N. Moreover, if N is a number field then we write
for the integral closure of
[½] in N. For an integral ideal & of
K we denote the ray classfield of K with conductor & by K(&). Once and for all we fix a choice of embedding of K into the complex numbers
.