no. 1
Logarithmic density of a sequence of integers and density of its ratio set
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 309-318.

Nous donnons des conditions suffisantes pour que l’ensemble R(A) des fractions d’un ensemble d’entiers A soit dense dans ℝ + , en termes des densités logarithmiques de A. Ces conditions diffèrent sensiblement de celles précédemment obtenues en termes des densités asymptotiques.

In the paper sufficient conditions for the (R)-density of a set of positive integers in terms of logarithmic densities are given. They differ substantially from those derived previously in terms of asymptotic densities.

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     author = {Mi\v{s}{\'\i}k, Ladislav and T\'oth, J\'anos T.},
     title = {Logarithmic density of a sequence of integers and density of its ratio set},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {309--318},
     publisher = {Universit\'e Bordeaux I},
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Mišík, Ladislav; Tóth, János T. Logarithmic density of a sequence of integers and density of its ratio set. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 309-318. http://www.numdam.org/item/JTNB_2003__15_1_309_0/

[1] K. Knopp, Theory and Application of Infinite Series. Blackie & Son Limited, London and Glasgow, 2-nd English Edition, 1957. | Zbl

[2] O. Strauch, J.T. Tóth, 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. | MR | Zbl

[3] T Šalát, On ratio sets of sets of natural numbers. Acta Arith. 15 (1969), 173-278. | MR | Zbl

[4] T. Šalát, Quotientbasen und (R)-dichte mengen. Acta Arith. 19 (1971), 63-78. | MR | Zbl

[5] J.T. Tóth, Relation between (R)-density and the lower asymptotic density. Acta Math. Constantine the Philosopher University Nitra 3 (1998), 39-44.