Arithmetic characterizations of Sidon sets

Abstract

Let Ĝ be any discrete Abelian group. We give several arithmetic characterizations of Sidon sets in Ĝ. In particular, we show that a set Λ is a Sidon set iff there is a number δ > 0 such that any finite subset A of Λ contains a subset B ⊂ A with |B| ≥ δ|A| which is quasiindependent, i.e. such that the only relation of the form (Equation presented), with ελequal to ± 1 or 0, is the trivial one. © 1983 American Mathematical Society.