an:04014839
Zbl 0625.10046
Ruzsa, Imre Z.
Probabilistic constructions in additive number theory
EN
Journ??es arithm??tiques, Besan??on/France 1985, Ast??risque 147/148, 173-182 (1986).
1986
a
11B13 11A25 11K99 11B83
sum-sets; additive bases; asymptotic density; counting function; Schnirelman density
[For the entire collection see Zbl 0605.00004.]
The author uses a new, probabilistic approach for constructing a class of sets \(H\subseteq {\mathbb{Z}}\) with the property that, for any set \(A\subseteq {\mathbb{Z}}\) whose counting function A(x) is not bounded by any function g(x) with g(x)/log x \(\nearrow\) and g(x)/x \(\searrow 0\), both \(H+A\) and H-A have (asymptotically) many elements in a sense specified for either of the two cases.
The result yields solutions of several older problems in additive number theory including the existence of a sequence A of density 0 such that the Schnirelman density \(\sigma\) satisfies \(\sigma (A+B)>0\) for every base B.
B.Volkmann
Zbl 0605.00004