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.
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Acknowledgments
The problem of proving equidistribution was suggested to me by graduate advisor Soundararajan. The possibility of calculating a negative secondary term related to k-torsion was suggested to me by Akshay Venkatesh.
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This material is based upon work supported by the National Science Foundation under agreement No. DMS-1128155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
The author acknowledges the support of a Ric Weiland Fellowship during his graduate studies at Stanford University.
We use ♭ to restrict sums to fundamental discriminants.
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Hough, B. Equidistribution of bounded torsion CM points. JAMA 138, 765–797 (2019). https://doi.org/10.1007/s11854-019-0044-4
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DOI: https://doi.org/10.1007/s11854-019-0044-4