The formula of 8-ranks of tame kernels
Let \(d\) be a squarefree integer that can be written in the form \(d = u^2 - 2w^2\), and consider the quadratic number fields \(F = \mathbb Q(\sqrt{d}\,)\) and \(E = \mathbb Q(\sqrt{-d}\,)\). The author proves that the \(8\)-rank of \(K_2({\mathcal O}_F)\) and the \(8\)-rank of the class group of \(E\) in the strict sense differ at most by \(1\). The main tools are the results of \textit{H.~Qin} [J. Reine Angew. Math. 530, 105--144 (2001; Zbl 1003.11052)] as well as Rédei matrices and results on the solvability of ternary quadratic forms \(aX^2 + bY^2 + cZ^2 = 0\).
scientific article; zbMATH DE number 2159733