Event Type:

Number Theory Seminar

Date/Time:

Tuesday, May 19, 2015 - 16:00 to 17:00

Location:

Bat 150

Guest Speaker:

Institution:

Mathematics Department, Oklahoma State University

Abstract:

In earlier work with Clay Petsche, we established lower bounds for the heights of algebraic numbers under splitting conditions, such as being totally real or totally p-adic (all Galois conjugates of the number real or p-adic, respectively). These results depended on lower bounds for energy integrals over local fields, and thus applied only in the limit as the degree of the algebraic numbers tended to infinity. In this talk we will discuss some techniques in discrete energy approximation which can make this dependence quantitative, and some interesting problems that arise in this direction. (Joint work with L. Pottmeyer.)