Logarithmic density of a sequence of integers and density of its ratio set. (English) Zbl 1130.11304

The authors deal with the concepts: asymptotic density, logarithmic density and \((R)\)-density and the relations between them. A set \(A\subseteq\mathbb N\) is said to be \((R)\)-dense provided that the set \(R(A)= \{\frac ab\); \(a,b\in A\}\) is dense in \((0,+\infty)\). Note that a sufficient condition for the \((R)\)-density of a set \(A\) in terms of logarithmic densities mentioned at the beginning of the paper can be derived from the Corollary on p. 318.


11B05 Density, gaps, topology
11B75 Other combinatorial number theory
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