On the quotient sequence of sequences of integers

Rudolf Ahlswede; Levon H. Khachatrian; András Sárközy

Acta Arithmetica (1999)

  • Volume: 91, Issue: 2, page 117-132
  • ISSN: 0065-1036

How to cite

top

Rudolf Ahlswede, Levon H. Khachatrian, and András Sárközy. "On the quotient sequence of sequences of integers." Acta Arithmetica 91.2 (1999): 117-132. <http://eudml.org/doc/207343>.

@article{RudolfAhlswede1999,
author = {Rudolf Ahlswede, Levon H. Khachatrian, András Sárközy},
journal = {Acta Arithmetica},
keywords = {quotient set of a set; infinite quotient set; lower density; upper logarithmic density},
language = {eng},
number = {2},
pages = {117-132},
title = {On the quotient sequence of sequences of integers},
url = {http://eudml.org/doc/207343},
volume = {91},
year = {1999},
}

TY - JOUR
AU - Rudolf Ahlswede
AU - Levon H. Khachatrian
AU - András Sárközy
TI - On the quotient sequence of sequences of integers
JO - Acta Arithmetica
PY - 1999
VL - 91
IS - 2
SP - 117
EP - 132
LA - eng
KW - quotient set of a set; infinite quotient set; lower density; upper logarithmic density
UR - http://eudml.org/doc/207343
ER -

References

top
  1. [1] R. Ahlswede and L. H. Khachatrian, Classical results on primitive and recent results on cross-primitive sequences, in: The Mathematics of Paul Erdős, Vol. I, R. L. Graham and J. Nešetřil (eds.), Algorithms Combin. 13, Springer, 1997, 104-116. Zbl0882.11009
  2. [2] F. Behrend, On sequences of numbers not divisible by one another, J. London Math. Soc. 10 (1935), 42-44. Zbl61.0132.01
  3. [3] H. Davenport and P. Erdős, On sequences of positive integers, Acta Arith. 2 (1936), 147-151. Zbl0015.10001
  4. [4] P. Erdős, Note on sequences of integers no one of which is divisible by any other, J. London Math. Soc. 10 (1935), 126-128. Zbl61.0132.02
  5. [5] P. Erdős, A generalization of a theorem of Besicovitch, J. London Math. Soc. 11 (1936), 92-98. Zbl0014.01104
  6. [6] P. Erdős, On the distribution of additive functions, Ann. of Math. 97 (1946), 1-20. Zbl0061.07902
  7. [7] P. Erdős, A. Sárközy and E. Szemerédi, On the divisibility properties of sequences of integers I, Acta Arith. 11 (1966), 411-418. Zbl0146.27102
  8. [8] P. Erdős, A. Sárközy and E. Szemerédi, On divisibility properties of sequences of integers, in: Colloq. Math. Soc. János Bolyai 2, 1970, 35-49. Zbl0212.39704
  9. [9] H. Halberstam and K. F. Roth, Sequences, Springer, Berlin, 1983. 
  10. [10] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. 48 (1920), 76-92. Zbl46.0262.03
  11. [11] J. Kubilius, Probabilistic Methods in the Theory of Numbers, Amer. Math. Soc. Transl. Math. Monographs 11, Providence, 1964. Zbl0133.30203
  12. [12] C. Pomerance and A. Sárközy, On homogeneous multiplicative hybrid problems in number theory, Acta Arith. 49 (1988), 291-302. 
  13. [13] A. Sárközy, On divisibility properties of sequences of integers, in: The Mathematics of Paul Erdős, Vol. I, R. L. Graham and J. Nešetřil (eds.), Algorithms Combin. 13, Springer, 1997, 241-250. Zbl0868.11011
  14. [14] L. G. Sathe, On a problem of Hardy on the distribution of integers having given number of prime factors, J. Indian Math. Soc. 17 (1953), 63-141; and 18 (1954), 27-81. Zbl0051.28008
  15. [15] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.