English

Additive structure in convex sets

Combinatorics 2025-09-03 v1 Number Theory

Abstract

This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set AA containing Ω(A3/2)\Omega(|A|^{3/2}) three-term arithmetic progressions.

Keywords

Cite

@article{arxiv.2509.01568,
  title  = {Additive structure in convex sets},
  author = {Thomas F. Bloom and Jakob Führer and Oliver Roche-Newton},
  journal= {arXiv preprint arXiv:2509.01568},
  year   = {2025}
}
R2 v1 2026-07-01T05:15:41.688Z