Affine symmetric spaces and 2-torsion in the class group of unit-monogenized cubic fields

Davenport’s lemma has been a crucial ingredient in recent applications of geometry of numbers to arithmetic statistics. The lemma estimates, with error-term, the number of lattice points contained in bounded semi-algebraic regions of ℝn in terms of the volumes of these regions and their projections to coordinate subspaces. In this talk, I will describe an application of geometry of numbers to a non-Euclidean setting (in which Davenport’s lemma does not apply) by explaining how to bound the average number of 2-torsion elements in the class group of unit-monogenized cubic fields. The proof proceeds by replacing Davenport’s lemma with counting results for affine symmetric spaces. Joint work with Iman Setayesh, Arul Shankar, and Ashvin Swaminathan.

Date

Affiliation

Member, School of Mathematics

Speakers

Artane Siad