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

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.

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.

@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},
     doi = {10.5802/jtnb.404},
     zbl = {02058871},
     mrnumber = {2019018},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.404/}
}
TY  - JOUR
TI  - Logarithmic density of a sequence of integers and density of its ratio set
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2003
DA  - 2003///
SP  - 309
EP  - 318
VL  - 15
IS  - 1
PB  - Université Bordeaux I
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.404/
UR  - https://zbmath.org/?q=an%3A02058871
UR  - https://www.ams.org/mathscinet-getitem?mr=2019018
UR  - https://doi.org/10.5802/jtnb.404
DO  - 10.5802/jtnb.404
LA  - en
ID  - JTNB_2003__15_1_309_0
ER  - 
%0 Journal Article
%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://doi.org/10.5802/jtnb.404
%R 10.5802/jtnb.404
%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, Volume 15 (2003) no. 1, pp. 309-318. doi : 10.5802/jtnb.404. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.404/

[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.

Cited by Sources: