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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.

MSC:

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

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