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.

@article{JTNB_2003__15_1_309_0,
     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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     year = {2003},
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     url = {http://www.numdam.org/item/JTNB_2003__15_1_309_0/}
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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/

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