New bounds for the Furstenberg-S\'ark\"ozy theorem
Number Theory
2025-01-13 v2
Abstract
Suppose that has no two elements differing by a square. Then .
Keywords
Cite
@article{arxiv.2411.17448,
title = {New bounds for the Furstenberg-S\'ark\"ozy theorem},
author = {Ben Green and Mehtaab Sawhney},
journal= {arXiv preprint arXiv:2411.17448},
year = {2025}
}
Comments
35 pages; new version improves exponent from $1/4 - o(1)$ to $1/2$