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

Servat Nyandwi
2003 Publications de l'Institut Mathématique (Beograd)  
We use the saddle-point method (due to Hildebrand-Tenenbaum [3]) to study the asymptotic behaviour of P n6x,P (n)6y τ k (n) for any k > 0 fixed, where P (n) is the greatest prime factor of n and τ k is Piltz' function. We generalize all results in [3] , where the case k = 1 has been treated.
doi:10.2298/pim0374037n fatcat:4dovw2am4vba5mzzuivccw44yq