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 + , 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 = {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/}
}
TY  - JOUR
AU  - Ladislav Mišík
AU  - János T. Tóth
TI  - Logarithmic density of a sequence of integers and density of its ratio set
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2003
SP  - 309
EP  - 318
VL  - 15
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_309_0/
LA  - en
ID  - JTNB_2003__15_1_309_0
ER  - 
%0 Journal Article
%A Ladislav Mišík
%A János T. Tóth
%T Logarithmic density of a sequence of integers and density of its ratio set
%J Journal de théorie des nombres de Bordeaux
%D 2003
%P 309-318
%V 15
%N 1
%I Université Bordeaux I
%U https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_309_0/
%G en
%F JTNB_2003__15_1_309_0
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/

[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.