Session I.2 - Computational Number Theory
Tuesday, June 13, 15:00 ~ 15:30
Exceptional Units from Geometry
Nicholas Triantafillou
Center for Communications Research - Princeton, USA - This email address is being protected from spambots. You need JavaScript enabled to view it.
We describe a geometric approach to construct explicit infinite families of number fields with large Lenstra constant (i.e. containing large sets of integers whose pairwise differences are units) and whose rings of integers contain many exceptional units. For example, by considering integral points on an appropriate model of the modular curve $X_1(11)$ punctured at its 5 rational points, we produce 80 infinite families of sextic number fields, each with Lenstra constant at least 6 and each containing at least 60 exceptional units. We will also discuss applications to studying torsion subgroups on elliptic curves over number fields.
Joint work with Dino Lorenzini (University of Georgia, USA).