• Corpus ID: 239016095

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

  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},
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… 
1 Citations
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