A Fourier-Free Density-Increment Proof of Roth's Theorem
Combinatorics
2026-05-20 v1 Number Theory
Abstract
We give an elementary, Fourier-free proof of Roth's theorem. The proof follows Roth's original density-increment strategy, but replaces the usual Fourier-analytic step with a direct combinatorial argument involving averages over sub-progressions.
Keywords
Cite
@article{arxiv.2605.19310,
title = {A Fourier-Free Density-Increment Proof of Roth's Theorem},
author = {Mark Lewko},
journal= {arXiv preprint arXiv:2605.19310},
year = {2026}
}
Comments
10 pages, no figures