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For each odd prime $p$, we conjecture the distribution of the $p$-torsionsubgroup of $K_{2n}(\mathcal{O}_F)$ as $F$ ranges over real quadratic fields,or over imaginary quadratic fields. We then prove that the average size of the$3$-torsion subgroup of $K_{2n}(\mathcal{O}_F)$ is as predicted by thisconjecture.

Statistics of $K$-groups modulo $p$ for the ring of integers of a varying quadratic number field