# Geometry-of-numbers methods in the cusp and applications to class groups

@inproceedings{Shankar2021GeometryofnumbersMI, title={Geometry-of-numbers methods in the cusp and applications to class groups}, author={Arul Shankar and Artane Siad and Ashvin A. Swaminathan and Ila Varma}, year={2021} }

In this article, we compute the mean number of 2-torsion elements in class groups of monogenized cubic orders, when such orders are enumerated by height. In particular, we show that the average size of the 2-torsion subgroup in the class group increases when one ranges over all monogenized cubic orders instead of restricting to the family of monogenized cubic fields (or equivalently, monogenized maximal cubic orders) as determined in [8]. In addition, for each fixed odd integer n ≥ 3, we bound…

## One Citation

Average $2$-Torsion in Class Groups of Rings Associated to Binary $n$-ic Forms.

- Mathematics
- 2020

Let $n \geq 3$. We prove several theorems concerning the average behavior of the $2$-torsion in class groups of rings defined by integral binary $n$-ic forms having any fixed odd leading coefficient…

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