Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions
Number Theory
2021-09-02 v2 Combinatorics
Abstract
We show that if contains no non-trivial three-term arithmetic progressions then for some absolute constant . In particular, this proves the first non-trivial case of a conjecture of Erd\H{o}s on arithmetic progressions.
Cite
@article{arxiv.2007.03528,
title = {Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions},
author = {Thomas F. Bloom and Olof Sisask},
journal= {arXiv preprint arXiv:2007.03528},
year = {2021}
}