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

## TL;DR

This paper conjectures the distribution of $p$-torsion subgroups in higher algebraic K-groups of quadratic number fields and proves the average size for the case p=3 aligns with the conjecture.

## Contribution

It introduces a conjecture on the distribution of $p$-torsion in K-groups for quadratic fields and confirms the average size for p=3 matches this conjecture.

## Key findings

- Conjectured distribution of $p$-torsion in K-groups for quadratic fields.
- Proved the average size of 3-torsion subgroup matches the conjecture.
- Provides evidence supporting the conjecture for $p=3$.

## 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.