Distribution of values of Euler's function over integers free of large prime factors

A. Smati; J. Wu

Acta Arithmetica (1996)

  • Volume: 77, Issue: 2, page 139-155
  • ISSN: 0065-1036

How to cite

top

A. Smati, and J. Wu. "Distribution of values of Euler's function over integers free of large prime factors." Acta Arithmetica 77.2 (1996): 139-155. <http://eudml.org/doc/206914>.

@article{A1996,
author = {A. Smati, J. Wu},
journal = {Acta Arithmetica},
keywords = {distribution of values; integers free of large prime factors; Euler's function; asymptotic results on counting functions},
language = {eng},
number = {2},
pages = {139-155},
title = {Distribution of values of Euler's function over integers free of large prime factors},
url = {http://eudml.org/doc/206914},
volume = {77},
year = {1996},
}

TY - JOUR
AU - A. Smati
AU - J. Wu
TI - Distribution of values of Euler's function over integers free of large prime factors
JO - Acta Arithmetica
PY - 1996
VL - 77
IS - 2
SP - 139
EP - 155
LA - eng
KW - distribution of values; integers free of large prime factors; Euler's function; asymptotic results on counting functions
UR - http://eudml.org/doc/206914
ER -

References

top
  1. [1] M. Balazard and A. Smati, Elementary proof of a theorem of Bateman, in: Analytic Number Theory, Proceedings of a Conference in Honor of Paul T. Bateman, B. Berndt, H. Diamond, H. Halberstam and A. Hildebrand (eds.), Urbana, 1989, Progr. Math. 85, Birkhäuser, 1990, 41-46. 
  2. [2] P. T. Bateman, The distribution of values of Euler's function, Acta Arith. 21 (1972), 329-345. Zbl0217.31901
  3. [3] N. G. de Bruijn, The asymptotic behaviour of a function occurring in the theory of primes, J. Indian Math. Soc. (N.S.) 15 (1951), 25-32. Zbl0043.06502
  4. [4] N. G. de Bruijn, On the number of positive integers ≤ x and free of prime factors > y, II, Nederl. Akad. Wetensch. Proc. Ser. A 69 (1966), 239-247. Zbl0139.27203
  5. [5] P. Erdős, Some remarks on Euler's ϕ-function and some related problems, Bull. Amer. Math. Soc. 51 (1945), 540-544. Zbl0061.08005
  6. [6] P. Erdős, A. Ivić and C. Pomerance, On sums involving reciprocals of the largest prime factor of an integer, Glas. Mat. Ser. III 21 (41) (1986), 283-300. 
  7. [7] A. Hildebrand, On the number of positive integers ≤ x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. Zbl0575.10038
  8. [8] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290. Zbl0601.10028
  9. [9] A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484. Zbl0797.11070
  10. [10] A. Ivić, On some estimates involving the number of prime divisors of an integer, Acta Arith. 49 (1987), 21-33. Zbl0573.10038
  11. [11] A. Ivić and G. Tenenbaum, Local densities over integers free of large prime factors, Quart. J. Math. Oxford Ser. (2) 37 (1986), 401-417. Zbl0604.10024
  12. [12] E. Saias, Entiers sans grand ni petit facteur premier III, Acta Arith. 71 (1995), 351-379. Zbl0854.11045
  13.  
  14. [14] G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995. 

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.