The formula of 8-ranks of tame kernels

In this paper, we always assume that and , d a squarefree integer, are quadratic number fields with d=u2−2w2, . This paper is mainly to give the formula: 8-rank of K2OF=8-rank of C(E)+a(F)+σ, where C(E) is the narrow class group of E, a(F) {−1,0,1} and σ {0,1}; moreover 8-rank of K2OF-8-rank of C(E) 1. This paper is also to show the relations among , the dyadic ideal class of C(E) and the dyadic ideal class of C(E′) for .