Equidistribution of bounded torsion CM points

TL;DR

This paper proves the equidistribution of certain CM points linked to 3-torsion class groups in imaginary quadratic fields, providing quantitative results, partial extensions, and empirical evidence for broader cases.

Contribution

It establishes the first quantitative equidistribution result for 3-torsion CM points and offers partial results and empirical support for general odd order cases.

Findings

Quantitative equidistribution of 3-torsion CM points

Partial results for arbitrary odd order ideals

Empirical evidence supporting broader conjectures

Abstract

Averaging over imaginary quadratic fields, we prove, quantitatively, the equidistribution of CM points associated to 3-torsion classes in the class group. We conjecture that this equidistribution holds for points associated to ideals of any fixed odd order. We prove a partial equidistribution result in this direction and present empirical evidence.