Valeur moyenne des fonctions de Piltz sur les entiers sans grand facteur premier
Hikma Smida
Acta Arithmetica, Tome 64 (1993), p. 21-50 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:206505
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     author = {Hikma Smida},
     title = {Valeur moyenne des fonctions de Piltz sur les entiers sans grand facteur premier},
     journal = {Acta Arithmetica},
     volume = {64},
     year = {1993},
     pages = {21-50},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav63i1p21bwm}
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Hikma Smida. Valeur moyenne des fonctions de Piltz sur les entiers sans grand facteur premier. Acta Arithmetica, Tome 64 (1993) pp. 21-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav63i1p21bwm/

[000] [1] K. Alladi, Asymptotic estimates of sums involving the Moebius function. II, Trans. Amer. Math. Soc. 272 (1982), 87-105. | Zbl 0499.10050

[001] [2] K. Alladi, An Erdős-Kac theorem for integers without large prime factors, Acta Arith. 49 (1987), 81-105.

[002] [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. | Zbl 0042.04204

[003] [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. | Zbl 0131.28703

[004] [5] J.-M. De Koninck and D. Hensley, Sums taken over n≤x with prime factors ≤y of zΩ(n), and their derivatives with respect to z, J. Indian Math. Soc. (N.S.) 42 (1978-79), 353-365.

[005] [6] W. J. Ellison et M. Mendès France, Les nombres premiers, Hermann, 1975. | Zbl 0313.10001

[006] [7] E. Fouvry et G. Tenenbaum, Diviseurs de Titchmarsh des entiers sans grand facteur premier, prépublication. | Zbl 0708.11043

[007] [8] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. 63 (1991), 449-494. | Zbl 0745.11042

[008] [9] D. G. Hazlewood, On integers all of whose prime factors are small, Bull. London Math. Soc. 5 (1973), 159-163. | Zbl 0276.10022

[009] [10] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207. | Zbl 0302.10037

[010] [11] D. G. Hazlewood, Sums over numbers with restricted prime factors, J. Number Theory 17 (1983), 350-365. | Zbl 0519.10032

[011] [12] D. Hensley, The convolution powers of the Dickman function, J. London Math. Soc. (2) 33 (1986), 395-406. | Zbl 0565.10041

[012] [13] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307. | Zbl 0575.10038

[013] [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. | Zbl 0675.34037

[014] [15] A. Hildebrand, On a problem of Erdős and Alladi, Monatsh. Math. 97 (1984), 119-124. | Zbl 0531.10046

[015] [16] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290. | Zbl 0601.10028

[016] [17] A. Hildebrand and G. Tenenbaum, On a class of differential-difference equations arising in number theory, prépublication. | Zbl 0797.11072

[017] [18] A. Ivić, On squarefree numbers with restricted prime factors, Studia Sci. Math. Hungar. 20 (1985), 189-192. | Zbl 0544.10043

[018] [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. | Zbl 0604.10024

[019] [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. | Zbl 0204.06502

[020] [21] E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78-99. | Zbl 0676.10028

[021] [22] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. (N.S.) 18 (1954), 83-87.

[022] [23] H. Smida, Sur les puissances de convolution de la fonction de Dickman, Acta Arith. 59 (1991), 123-143. | Zbl 0881.11069

[023] [24] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Institut Elie Cartan 13, Univ. de Nancy 1, 1990.

[024] [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.

[025] [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.

[026] [27] D. T. Widder, The Laplace Transform, Princeton University Press, 1946. | Zbl 0060.24801

[027] [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). | Zbl 0751.11044

[028] [29] T. Z. Xuan, The average order of dk(n) over integers free of large prime factors, Acta Arith. 55 (1990), 249-260.