Number Theory seminar: Nick Andersen (BYU)
- Event Type
- Lecture
- Sponsor
- Mathematics Department
- Location
- Altgeld 241
- Date
- Apr 25, 2023 11:00 am
- Speaker
- Nick Andersen
- Contact
- Kevin Ford
- ford126@illinois.edu
- Views
- 26
- Originating Calendar
- Number Theory Seminar Calendar
Title: Geometry of numbers and L^p best approximations
Abstract: A theorem of Davenport and Schmidt treats the question of when Dirichlet’s theorem on the rational approximation of irrationals can be improved and if so, by how much. We consider a generalization of this question in the context of the geometry of numbers in R^2, with the sup-norm replaced by the L^p norm for p \geq 1. We obtain sharp bounds for how much improvement is possible under various conditions. The proofs use semi-regular continued fractions that are characterized by a certain best approximation property determined by the norm. We conclude by extending some of the results to the non-convex case 0<p<1. This is joint work with W. Duke, Z. Hacking, and A. Woodall.