arXiv:2302.07211math.NT
The Kelley--Meka bounds for sets free of three-term arithmetic progressions
Abstract
We give a self-contained exposition of the recent remarkable result of Kelley and Meka: if $A\subseteq \{1,\ldots,N\}$ has no non-trivial three-term arithmetic progressions then $\lvert A\rvert \leq \exp(-c(\log N)^{1/12})N$ for some constant $c>0$. Although our proof is identical to that of Kelley and Meka in all of the main ideas, we also incorporate some minor simplifications relating to Bohr sets. This eases some of the technical difficulties tackled by Kelley and Meka and widens the scope of their method. As a consequence, we improve the lower bounds for finding long arithmetic progressions in $A+A+A$, where $A\subseteq \{1,\ldots,N\}$.
Plus much shorter write-up from Bloom and Sisask: https://arxiv.org/abs/2302.07211
n4r9View on HNParent context
I think you mean this one: https://arxiv.org/abs/2302.07211
red_trumpetView on HNParent context
automatic conversion to web page available at https://ar5iv.labs.arxiv.org/html/2302.07211 (more info about the conversions at https://ar5iv.labs.arxiv.org)
rmlView on HNParent context
See also, ArΧiv Vanity: https://www.arxiv-vanity.com/papers/2302.07211/
satvikpendemView on HNParent context