On the 4-rank of the Tame Kernel K2(image) in Positive Definite Terms Original Research Article

The paper is about the structure of the tame kernel K2(image) for certain quadratic number fields. There has been recent progress in making explicit the 4-rank of the tame kernel of quadratic number fields and even in obtaining results about the 8-rank. The emphasis of this paper is to determine the 4-rank of the tame kernel in definite terms. Our characterizations are in terms of positive definite binary quadratic forms X2+32Y2, X2+2pY2, 2X2+pY2 over image. The results make numerical computations readily available, and the characterizations might generate some interest in “density results” concerning the 4-rank of tame kernels.