Evaluation effective du nombre d'entiers n tels que φ(n) ≤ x

ArticleOriginal scientific text

Title

Authors ¹

Département de Mathématiques, Faculté des Sciences de Limoges, 123, Avenue Albert Thomas, 87060 Limoges Cedex, France

M. Balazard and A. Smati, Elementary proof of a theorem of Bateman, dans : Analytic Number Theory, Proc. Conf. in Honor of Paul T. Bateman, Allerton Park, Ill., 1989, Progr. Math. 85, Birkhäuser, Boston 1990, 41-46.
P. T. Bateman, The distribution of values of the Euler function, Acta Arith. 21 (1972), 329-345.
R. E. Dressler, A density which counts multiplicity, Pacific J. Math. 34 (1970), 371-378.
P. Erdős, Some remarks on Euler's ϕ-function and some related problems, Bull. Amer. Math. Soc. 51 (1945), 540-544.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford 1979.
J.-L. Nicolas, Distribution des valeurs de la fonction d'Euler, Enseign. Math. 30 (1984), 331-338.
D. P. Parent, Exercises de théorie des nombres, Gauthier-Villars, Paris 1978.
H. Riesel, Prime Numbers and Computer Methods for Factorization, Birkhäuser, 1985.
J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.
A. Smati, Répartition des valeurs de la fonction d'Euler, Enseign. Math. 35 (1989), 61-76.
G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. Elie Cartan 13, Université de Nancy, 1990