Valeur moyenne des fonctions de Piltz sur les entiers sans grand facteur premier

 Access to full text

 Full (PDF)

1. [1] K. Alladi, Asymptotic estimates of sums involving the Moebius function. II, Trans. Amer. Math. Soc. 272 (1982), 87-105. Zbl0499.10050
2. [2] K. Alladi, An Erdős-Kac theorem for integers without large prime factors, Acta Arith. 49 (1987), 81-105. 
3. [3] N. G. de Bruijn, On the number of positive integers ≤x and free of prime factors >y, Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951), 50-60. Zbl0042.04204
4. [4] N. G. de Bruijn and Y. H. van Lint, Incomplete sums of multiplicative functions. I, II, Nederl. Akad. Wetensch. Proc. Ser. A 67 (1964), 339-347; 348-359. Zbl0131.28703
5. [5] J.-M. De Koninck and D. Hensley, Sums taken over n≤x with prime factors ≤y of $z^{\Omega }\left(n\right)$, and their derivatives with respect to z, J. Indian Math. Soc. (N.S.) 42 (1978-79), 353-365. 
6. [6] W. J. Ellison et M. Mendès France, Les nombres premiers, Hermann, 1975. Zbl0313.10001
7. [7] E. Fouvry et G. Tenenbaum, Diviseurs de Titchmarsh des entiers sans grand facteur premier, prépublication. Zbl0708.11043
8. [8] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. 63 (1991), 449-494. Zbl0745.11042
9. [9] D. G. Hazlewood, On integers all of whose prime factors are small, Bull. London Math. Soc. 5 (1973), 159-163. Zbl0276.10022
10. [10] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207. Zbl0302.10037
11. [11] D. G. Hazlewood, Sums over numbers with restricted prime factors, J. Number Theory 17 (1983), 350-365. Zbl0519.10032
12. [12] D. Hensley, The convolution powers of the Dickman function, J. London Math. Soc. (2) 33 (1986), 395-406. Zbl0565.10041
13. [13] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. Zbl0575.10038
14. [14] A. Hildebrand, The asymptotic behavior of the solutions of a class of differential-difference equations, J. London Math. Soc. (2) 42 (1990), 11-31. Zbl0675.34037
15. [15] A. Hildebrand, On a problem of Erdős and Alladi, Monatsh. Math. 97 (1984), 119-124. Zbl0531.10046
16. [16] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290. Zbl0601.10028
17. [17] A. Hildebrand and G. Tenenbaum, On a class of differential-difference equations arising in number theory, prépublication. Zbl0797.11072
18. [18] A. Ivić, On squarefree numbers with restricted prime factors, Studia Sci. Math. Hungar. 20 (1985), 189-192. Zbl0544.10043
19. [19] 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
20. [20] B. V. Levin and A. S. Faĭnleĭb, Application of some integral equations to problems in number theory, Russian Math. Surveys 22 (3) (1967), 119-204. Zbl0204.06502
21. [21] E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78-99. Zbl0676.10028
22. [22] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. (N.S.) 18 (1954), 83-87. 
23. [23] H. Smida, Sur les puissances de convolution de la fonction de Dickman, Acta Arith. 59 (1991), 123-143. Zbl0881.11069
24. [24] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Institut Elie Cartan 13, Univ. de Nancy 1, 1990. 
25. [25] G. Tenenbaum, La méthode du col en théorie analytique des nombres, dans: Séminaire de Théorie des Nombres, Paris 1986-87, Progr. Math. 75, Birkhäuser, 1988, 411-441. 
26. [26] G. Tenenbaum, Sur un problème d'Erdős et Alladi, dans: Séminaire de Théorie des Nombres, Paris 1988-1989, Progr. Math. 91, Birkhäuser, 1990, 221-239. 
27. [27] D. T. Widder, The Laplace Transform, Princeton University Press, 1946. Zbl0060.24801
28. [28] T. Z. Xuan, The average order of divisor functions over integers without large prime factors, Chinese Ann. Math. Ser. A 12 (1991), suppl., 28-33 (in Chinese). Zbl0751.11044
29. [29] T. Z. Xuan, The average order of $d_k\left(n\right)$ over integers free of large prime factors, Acta Arith. 55 (1990), 249-260. 

1. Mongi Naimi, Répartition en moyenne de certaines fonctions arithmétiques sur l'ensemble des entiers sans grand facteur premier
2. Eric Saias, Entiers sans grand ni petit facteur premier II
3. Joseph Basquin, Loi de répartition moyenne des diviseurs des entiers friables
4. Eira J. Scourfield, On ideals free of large prime factors
5. Adolf Hildebrand, Gerald Tenenbaum, Integers without large prime factors