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

doi:10.2140/TUNIS.2020.2.287

Open AccessJournal ArticleDOI

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

Bruce W. Jordan, +4 more

- 01 Mar 2017 -

arXiv: Number Theory

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TLDR

In this article, the authors conjecture that the distribution of the torsion subgroup of the odd prime k-2n/k-1 group of k-1/k 2n (K 2n) (mathcal{O}_F) ranges over real quadratic fields, or over imaginary quadrastic fields.

Abstract:

For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup 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 this conjecture.

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