On Tame Kernel and Class Group in Terms of Quadratic Forms Original Research Article

The paper is to investigate the structure of the tame kernel K2OF for certain quadratic number fields F, which extends the scope of Conner and Hurrelbrink (J. Number Theory88 (2001), 263–282). We determine the 4-rank and the 8-rank of the tame kernel, the Tate kernel, and the 2-part of the class group. Our characterizations are in terms of binary quadratic forms X2+32Y,X2+64Y2,X2+2Py2,2X2+Py2,X2−2Py2,2X2−Py2. The results are very useful for numerical computations.