Ethan Ackelsberg

Furstenberg--Sárközy theorem and partition regularity of polynomial equations over finite fields

2023 · arXiv (Cornell University)

We prove new combinatorial results about polynomial configurations in large subsets of finite fields. Bergelson--Leibman--McCutcheon (2005) showed that for any polynomial $P(x) \in \mathbb{Z}[x]$ with $P(0) = 0$, if $A \subseteq \mathbb{F}_q$ is a subset …