On the distribution of class groups of number fields

TL;DR

This paper proposes a modified Cohen--Lenstra heuristic for class groups of number fields accounting for roots of unity, supported by computational data showing strong agreement.

Contribution

It introduces a new heuristic adjustment for class group distributions when roots of unity are present, backed by extensive computational evidence.

Findings

Modified heuristic aligns well with computational data

Roots of unity significantly influence class group distribution

Empirical evidence supports the proposed adjustment

Abstract

We propose a modification of the predictions of the Cohen--Lenstra heuristic for class groups of number fields in the case where roots of unity are present in the base field. As evidence for this modified formula we provide a large set of computational data which show close agreement.