Title: Uniform Distribution and Roth's Theorem
Author: Yingnan Wang
Abstract: In this lecture we talk about a proof of Roth's Theorem given by Andrew Granville. Granville first gives an introduction to Weyl's famous criterion for recognizing uniform distribution modulo one. When he considers uniform distribution modulo N, he formulates an analogy to Weyl's criterion along the lines: The Fourier transforms of A are all small if and only if A and all of its dilates are uniform distributed. This idea is essential to his proof of Roth's Theorem.
Attachment: Uniform Distribution and Roth's Theorem