The Structure of the Tame Kernels of Quadratic Number Fields (III)

Abstract

Let F be an imaginary quadratic number field and K 2 O F the tame kernel of F. In this article, we determine all possible values of r 4(K 2 O F ) for each type of imaginary quadratic number field F. In particular, for each type of imaginary quadratic number field we give the maximum possible value of r 4(K 2 O F ) and show that each integer between the lower and upper bounds occurs as a value of the 4-rank of K 2 O F for infinitely many imaginary quadratic number fields F.