New lower bounds for $r_3(N)$

Zach Hunter

Type: Preprint

Publication Date: 2024-01-29

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2401.16106

Abstract

We develop recent ideas of Elsholtz, Proske, and Sauermann to construct denser subsets of $\{1,\dots,N\}$ that lack arithmetic progressions of length $3$. This gives the first quasipolynomial improvement since the original construction of Behrend.

Locations

arXiv (Cornell University) - View - PDF

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