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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Département de Mathématiques, Unité associée au CNRS, URA 1586, Université Limoges, 87060 Limoges Cedex, France
  2. Laboratoire de Mathématiques, Institut Élie Cartan - UMR CNRS 9973, Université Henri Poincaré, Nancy 1, 54506 Vandœuvre-lès-Nancy, France

Bibliography

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  2. P. T. Bateman, The distribution of values of Euler's function, Acta Arith. 21 (1972), 329-345.
  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.
  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.
  5. P. Erdős, Some remarks on Euler's ϕ-function and some related problems, Bull. Amer. Math. Soc. 51 (1945), 540-544.
  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. A. Hildebrand, On the number of positive integers ≤ x and free of prime factors >y, J. Number Theory 22 (1986), 289-307.
  8. A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290.
  9. A. Hildebrand and G. Tenenbaum, Integers without large prime factors, J. Théor. Nombres Bordeaux 5 (1993), 411-484.
  10. A. Ivić, On some estimates involving the number of prime divisors of an integer, Acta Arith. 49 (1987), 21-33.
  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.
  12. E. Saias, Entiers sans grand ni petit facteur premier III, Acta Arith. 71 (1995), 351-379.
  13. A. Smati and J. Wu, Distribution of values of Euler's function in algebraic number fields, Prépublication du Laboratoire d'Arithmétique, Calcul Formel & Optimisation, Université Limoges, 94/N!$!°4.
  14. G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995.
Acta Arithmetica
1996/77/2
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Pages:
139-155
Main language of publication
English
Received
1995-06-26
Published
1996
Exact and natural sciences