On the Distribution of Class Groups of Number Fields

Abstract

We propose a modification of the predictions of the Cohen-Lenstra heuristic for class groups of number fields in the case that roots of unity are present in the base field. As evidence for this modified formula we provide a large set of computational data that show close agreement with it. Furthermore, our predicted formula agrees with results on class groups of function fields in positive characteristic for which the base field contains appropriate roots of unity.

Keywords:

• Class groups
• Cohen-Lenstra heuristic
• computational