Fourier Transforms on Finite Fields and an Application of Stickelberger's Theorem

Speaker: Professor Gary McGuire (UCD, Claude Shannon Institute)

Time: 5:00PM
Date: Wed 25th April 2007

Location: Mathematical Sciences Seminar Room

We will introduce the topic of Fourier transforms on finite fields. We explain an approach to determining the Fourier spectrum using Gauss sums and p-adic valued characters on the
multiplicative group of a finite field, and Stickelberger's theorem. We apply the techniques to certain functions on fields of characteristic 2. We shall conclude with some open problems, in both odd and even characteristic.

(This talk is part of the K-Theory, Quadratic Forms and Number Theory series.)