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

Journal de théorie des nombres de Bordeaux (2003)

- Volume: 15, Issue: 1, page 309-318
- ISSN: 1246-7405

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topMišík, Ladislav, and Tóth, János T.. "Logarithmic density of a sequence of integers and density of its ratio set." Journal de théorie des nombres de Bordeaux 15.1 (2003): 309-318. <http://eudml.org/doc/249074>.

@article{Mišík2003,

abstract = {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.},

author = {Mišík, Ladislav, Tóth, János T.},

journal = {Journal de théorie des nombres de Bordeaux},

language = {eng},

number = {1},

pages = {309-318},

publisher = {Université Bordeaux I},

title = {Logarithmic density of a sequence of integers and density of its ratio set},

url = {http://eudml.org/doc/249074},

volume = {15},

year = {2003},

}

TY - JOUR

AU - Mišík, Ladislav

AU - Tóth, János T.

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

JO - Journal de théorie des nombres de Bordeaux

PY - 2003

PB - Université Bordeaux I

VL - 15

IS - 1

SP - 309

EP - 318

AB - 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.

LA - eng

UR - http://eudml.org/doc/249074

ER -

## References

top- [1] K. Knopp, Theory and Application of Infinite Series. Blackie & Son Limited, London and Glasgow, 2-nd English Edition, 1957. Zbl0042.29203
- [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. Zbl0923.11027MR1904872
- [3] T Šalát, On ratio sets of sets of natural numbers. Acta Arith.15 (1969), 173-278. Zbl0177.07001MR242756
- [4] T. Šalát, Quotientbasen und (R)-dichte mengen. Acta Arith.19 (1971), 63-78. Zbl0218.10071MR292788
- [5] J.T. Tóth, Relation between (R)-density and the lower asymptotic density. Acta Math. Constantine the Philosopher University Nitra3 (1998), 39-44.

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