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

Ladislav Mišík; János T. Tóth

Journal de théorie des nombres de Bordeaux (2003)

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

Abstract

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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.

How to cite

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Mišík, 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

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  1. [1] K. Knopp, Theory and Application of Infinite Series. Blackie & Son Limited, London and Glasgow, 2-nd English Edition, 1957. Zbl0042.29203
  2. [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. [3] T Šalát, On ratio sets of sets of natural numbers. Acta Arith.15 (1969), 173-278. Zbl0177.07001MR242756
  4. [4] T. Šalát, Quotientbasen und (R)-dichte mengen. Acta Arith.19 (1971), 63-78. Zbl0218.10071MR292788
  5. [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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