Asymptotics of $p$-torsion subgroup sizes in class groups of monogenized cubic fields

Mikaeel Yunus

Asymptotics of $p$-torsion subgroup sizes in class groups of monogenized cubic fields

Number Theory 2021-02-01 v1

Authors: Mikaeel Yunus

Abstract

Bhargava, Hanke, and Shankar have recently shown that the asymptotic average $2$ -torsion subgroup size of the family of class groups of monogenized cubic fields with positive and negative discriminants is $3/2$ and $2$ , respectively. In this paper, we provide strong computational evidence for these asymptotes. We then develop a pair of novel conjectures that predicts, for $p$ prime, the asymptotic average $p$ -torsion subgroup size in class groups of monogenized cubic fields.

Keywords

p-torsion subgroup class groups monogenized cubic fields asymptotic average discriminant conjectures

Cite

@article{arxiv.2101.12296,
  title  = {Asymptotics of $p$-torsion subgroup sizes in class groups of monogenized cubic fields},
  author = {Mikaeel Yunus},
  journal= {arXiv preprint arXiv:2101.12296},
  year   = {2021}
}

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