Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields

Christian Elsholtz, Zach Hunter, Laura Proske +1

We prove new lower bounds on the maximum size of subsets $A\subseteq \{1,\dots ,N\}$ or $A\subseteq {\mathbb{F}}_p^n$ not containing three-term arithmetic progressions. In the setting…