Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions.

By Thomas F. Bloom, Olof Sisask. 2020

60 citations recorded by the source corpus.

We show that if $A\subset \{1,\ldots,N\}$ contains no non-trivial three-term arithmetic progressions then $\lvert A\rvert \ll N/(\log N)^{1+c}$ for some absolute constant $c>0$. In particular, this proves the first non-trivial case of a conjecture of Erdős on arithmetic progressions.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/08b9bdef09b215e6d324c82847b1ca663f100e27