What is the structure of K if \(K+K\) is small ? (English) Zbl 0625.10045

Freiman, Gregory A.

Number theory, Semin. New York 1984/85, Lect. Notes Math. 1240, 109-134 (1987).

[For the entire collection see Zbl 0605.00005.]
The fact that, if a large finite set \(K\subseteq {\mathbb{Z}}\) is such that \(| K+K | : | K |\) is small then K is a “short” arithmetic progression, has been generalized by the author [Foundations of a structural theory of set addition (Providence 1973; Zbl 0271.10044); p. 54-73 (Russian original: Kazan’ 1966; Zbl 0203.353)] to sets of lattice- points. The present paper gives a simplified proof of this theorem.

Reviewer: B.Volkmann

MSC:

11B05

Density, gaps, topology

Keywords:

sum-sets; addition of sets; sets of lattice-points

Citations:

Zbl 0605.00005; Zbl 0271.10044; Zbl 0203.353