Mean value of Piltz' function over integers free of large prime factors

Servat Nyandwi

Type: Article

Publication Date: 2003-01-01

Citations: 0

DOI: https://doi.org/10.2298/pim0374037n

Abstract

We use the saddle-point method (due to Hildebrand?Tenenbaum [3]) to study the asymptotic behavior of ?n?x, p(n)?y ?k(n) for any k > 0 fixed, where P(n) is the greatest prime factor of n and ?k is Piltz' function. We generalize all results in [3], where the case k = 1 has been treated.

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Works Cited by This (10)

Action	Title	Year	Authors
+ PDF Chat	On integers free of large prime factors	1986	Adolf Hildebrand Gérald Tenenbaum
+	On the number of positive integers ≦ x and free of prime factors > y	1986	Adolf Hildebrand
+	Numbers with small prime factors, and the least 𝑘th power non-residue	1971	Karl K. Norton
+	Introduction à la théorie analytique et probabiliste des nombres	2015	Gérald Tenenbaum
+	Integers free of large prime factors and the Riemann hypothesis	1984	Adolf Hildebrand
+	Sur le nombre des entiers sans grand facteur premier	1989	Éric Saïas
+ PDF Chat	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum
+	On The Number of Positive Integers ≤ x and Free of Prime Factors > y	1951	N.G. de Bruijn
+ PDF Chat	Valeur moyenne des fonctions de Piltz sur les entiers sans grand facteur premier	1993	Hikma Smida
+	On Integers Free of Large Prime Factors	1986	Adolf Hildebrand Gérald Tenenbaum