An improvement to the Kelley-Meka bounds on three-term arithmetic progressions

Abstract: In a recent breakthrough Kelley and Meka proved a quasipolynomial upper bound for the density of sets of integers without non-trivial three-term arithmetic progressions. We present a simple modification to their method that strengthens their conclusion, in particular proving that if $A\subset{1,\ldots,N}$ has no non-trivial three-term arithmetic progressions then [\lvert A\rvert \leq \exp(-c(\log N)^{1/9})N] for some $c>0$.