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

2021/01/28 by Yunus, Mikaeel
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.12296

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.

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