Student Number Theory Seminar

Monday, July 17, 2017 10:00 am - 10:00 am EDT (GMT -04:00)

Stephen Wen, University of Waterloo

An analog of Sarközy's theorem on squares in difference sets

We will follow a paper by Yu-Ru Liu and Thái Hoàng Lê in which we examine the difference sets of subsets of $\mathbb{F}_q[t]$. We will find a sufficient condition on the density of a subset $A$ in the set of polynomials of degree strictly less than $N$, denoted $\mathbb{G}_N$, so that $A-A$ must contain a perfect square. We will do this by bounding the density of sets $A$ such that $A-A$ has no perfect square. We will use the polynomial Hardy-Littlewood circle method along with density increment technology developed by Pintz, Steiger, and Szemerédi.

MC 5403