Logarithmic density of a sequence of integers and density of its ratio set

Ladislav Mišík; János T. Tóth

Ladislav Mišík ; János T. Tóth

Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 309-318.

Résumé
Abstract

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.

MR Zbl

@article{JTNB_2003__15_1_309_0,
     author = {Ladislav Mi\v{s}{\'\i}k and J\'anos T. T\'oth},
     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},
     volume = {15},
     number = {1},
     year = {2003},
     zbl = {02058871},
     mrnumber = {2019018},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_309_0/}
}

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Ladislav Mišík; János T. Tóth. 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. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_309_0/

Bibliographie
Cité par

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