A Weyl-type inequality for irreducible elements in function fields, with applications

Abstract: We establish a Weyl-type estimate for exponential sums over irreducible elements in function fields. As an application, we generalize an equidistribution theorem of Rhin. Our estimate works for polynomials with degree higher than the characteristic of the field, a barrier to the traditional Weyl differencing method. In this talk, we briefly introduce Lê-Liu-Wooley’s original argument for ordinary Weyl sums (taken over all elements), and how we generalize it to estimate bilinear exponential sums with general coefficients. This is joint work with Jérémy Campagne (Waterloo), Thái Hoàng Lê (Mississippi) and Yu-Ru Liu (Waterloo).

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar