On the 2-primary part of tame kernels of real quadratic fields

Abstract

Let \(F = Q\left( {\sqrt p } \right)\), where p = 8t+1 is a prime. In this paper, we prove that a special case of Qin’s conjecture on the possible structure of the 2-primary part of K2OF up to 8-rank is a consequence of a conjecture of Cohen and Lagarias on the existence of governing fields. We also characterize the 16-rank of K2OF, which is either 0 or 1, in terms of a certain equation between 2-adic Hilbert symbols being satisfied or not.