New lower bounds for $r_3(N)$
Combinatorics
2024-07-03 v3 Number Theory
Abstract
We develop recent ideas of Elsholtz, Proske, and Sauermann to construct denser subsets of that lack arithmetic progressions of length . This gives the first quasipolynomial improvement since the original construction of Behrend.
Keywords
Cite
@article{arxiv.2401.16106,
title = {New lower bounds for $r_3(N)$},
author = {Zach Hunter},
journal= {arXiv preprint arXiv:2401.16106},
year = {2024}
}
Comments
11 pages, comments welcome! (in v2 we have corrected some typos in our proof of Proposition 1.3) v3 update: We have now merged our results with Elsholtz, Proske, and Sauermann, see arXiv:2401.12802