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

• Autorzy: Hikma Smida
• Języki publikacji: FR
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 63
• Numer: 1
• Strony: 21-50

Daty

wydano

1993

otrzymano

1991-10-08

Twórcy

autor

Hikma Smida

• Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060 Tunis, Tunisie

Bibliografia

• [1] K. Alladi, Asymptotic estimates of sums involving the Moebius function. II, Trans. Amer. Math. Soc. 272 (1982), 87-105.
• [2] K. Alladi, An Erdős-Kac theorem for integers without large prime factors, Acta Arith. 49 (1987), 81-105.
• [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.
• [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.
• [5] J.-M. De Koninck and D. Hensley, Sums taken over n≤x with prime factors ≤y of $z^Ω(n)$, and their derivatives with respect to z, J. Indian Math. Soc. (N.S.) 42 (1978-79), 353-365.
• [6] W. J. Ellison et M. Mendès France, Les nombres premiers, Hermann, 1975.
• [7] E. Fouvry et G. Tenenbaum, Diviseurs de Titchmarsh des entiers sans grand facteur premier, prépublication.
• [8] E. Fouvry et G. Tenenbaum, Entiers sans grand facteur premier en progressions arithmétiques, Proc. London Math. Soc. 63 (1991), 449-494.
• [9] D. G. Hazlewood, On integers all of whose prime factors are small, Bull. London Math. Soc. 5 (1973), 159-163.
• [10] D. G. Hazlewood, Sums over positive integers with few prime factors, J. Number Theory 7 (1975), 189-207.
• [11] D. G. Hazlewood, Sums over numbers with restricted prime factors, J. Number Theory 17 (1983), 350-365.
• [12] D. Hensley, The convolution powers of the Dickman function, J. London Math. Soc. (2) 33 (1986), 395-406.
• [13] A. Hildebrand, On the number of positive integers ≤x and free of prime factors >y, J. Number Theory 22 (1986), 289-307.
• [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.
• [15] A. Hildebrand, On a problem of Erdős and Alladi, Monatsh. Math. 97 (1984), 119-124.
• [16] A. Hildebrand and G. Tenenbaum, On integers free of large prime factors, Trans. Amer. Math. Soc. 296 (1986), 265-290.
• [17] A. Hildebrand and G. Tenenbaum, On a class of differential-difference equations arising in number theory, prépublication.
• [18] A. Ivić, On squarefree numbers with restricted prime factors, Studia Sci. Math. Hungar. 20 (1985), 189-192.
• [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.
• [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.
• [21] E. Saias, Sur le nombre des entiers sans grand facteur premier, J. Number Theory 32 (1989), 78-99.
• [22] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. (N.S.) 18 (1954), 83-87.
• [23] H. Smida, Sur les puissances de convolution de la fonction de Dickman, Acta Arith. 59 (1991), 123-143.
• [24] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Institut Elie Cartan 13, Univ. de Nancy 1, 1990.
• [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] 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] D. T. Widder, The Laplace Transform, Princeton University Press, 1946.
• [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).
• [29] T. Z. Xuan, The average order of $d_k(n)$ over integers free of large prime factors, Acta Arith. 55 (1990), 249-260.