New bounds for the Furstenberg-S\'ark\"ozy theorem

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2411.17448 v2 pith:REAQ32WJ submitted 2024-11-26 math.NT

Ben Green , Mehtaab Sawhney This is my paper · ORCID

classification math.NT

keywords boundsdifferingdotselementsfurstenberg-ssqrtsquaresubset

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

Suppose that $A \subset \{1,\dots, N\}$ has no two elements differing by a square. Then $|A| \ll N e^{-c\sqrt{\log N}}$.

Forward citations

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The sharp exponent for the minimal distance problem
math.CO 2026-07 accept novelty 8.0 of 10

The minimal distance problem has sharp exponent 2/3: lower-bound configurations of size n with separation n^{-2/3−o(1)} are constructed via trace-zero lattices in high-degree totally real number fields.