## 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
Full Text:

### References:

 [1] Knopp, K., Theory and Application of Infinite Series. Blackie & Son Limited, London and Glasgow, 2-nd English Edition, 1957. · Zbl 0042.29203 [2] Strauch, O., Tóth, J.T., Asymptotic density of A C N and density of the ratio set R(A). Acta Arith.87 (1998), 67-78. Corrigendum in Acta Arith.103 (2002), 191-200. · Zbl 0923.11027 [3] T, Šalát, On ratio sets of sets of natural numbers. Acta Arith.15 (1969), 173-278. · Zbl 0177.07001 [4] Šalát, T., Quotientbasen und (R)-dichte mengen. Acta Arith.19 (1971), 63-78. · Zbl 0218.10071 [5] Tóth, J.T., Relation between (R)-density and the lower asymptotic density. Acta Math. Constantine the Philosopher University Nitra3 (1998), 39-44.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.