Additive structure in convex sets

2025/09/01 by Bloom, Thomas F., Führer, Jakob, Roche-Newton, Oliver
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.01568

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 A containing Ω(|A|^3/2) three-term arithmetic progressions.

Citations

• Control and its applications in additive combinatorics
• Large Convex sets in Difference sets
• Some new results on the higher energies I
• A convex set with a rich difference
• On an application of higher energies to Sidon sets
• Additive and multiplicative Sidon sets
• On sumsets of convex sets

Related

• Additive structure in convex translates
• Structure in additively nonsmoothing sets
• Control and its applications in additive combinatorics
• Additively stable sets, critical sets for the 3k-4 theorem in ℤ and ℝ
• Local Differences Determined by Convex sets