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

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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

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  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. 

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