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

Speaker: Zenchao Ge

Date: Tue, Oct 17, 2023

Location: PIMS, University of Lethbridge, Online, Zoom

Conference: Lethbridge Number Theory and Combinatorics Seminar

Subject: Mathematics, Number Theory

Class: Scientific


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).

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