Tame kernels of quadratic number fields: numerical heuristics

Abstract

Basing on conjectures given by H. Cohen, H.W. Lenstra, Jr. and J. Martinet [2], [3], [4], [5] concerning the heuristics on class groups of number fields we deduce some quantitative conjectures on the statistical behaviour of orders of the tame kernel $K_{2}\mathcal{O}_{F}$ of the ring $\mathcal{O}_{F}$ of integers of quadratic number fields $F$ of discriminants $D, \vert D \vert \leq x$.

We investigate the number of $D$'s such that for $F = \mathbb{Q}(\sqrt{D})$ the order of $K_{2}\mathcal{O}_{F}$ is divisible by $3$.