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Let Ω(n) and ω(n) denote the number of distinct prime factors of the positive integer n, counted respectively with and without multiplicity. Let denote the Piltz function (which counts the number of ways of writing n as a product of k factors). We obtain a precise estimate of the sum
for a class of multiplicative functions f, including in particular , unconditionally if 1 ≤ k ≤ 3, and under some reasonable assumptions if k ≥ 4.
The result also applies to f(n) = φ(n)/n (where φ is the totient function), to (where is the sum of rth powers of divisors) and to functions related to the notion of exponential divisor. It generalizes similar results by J. Wu and Y.-K. Lau when f(n) = 1, respectively .
Rimer Zurita. "Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz." Acta Arithmetica 161.1 (2013): 69-100. <http://eudml.org/doc/278958>.
@article{RimerZurita2013, author = {Rimer Zurita}, journal = {Acta Arithmetica}, keywords = {divisor problems; Rényi problem; Piltz function; Lindelöf hypothesis}, language = {fre}, number = {1}, pages = {69-100}, title = {Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz}, url = {http://eudml.org/doc/278958}, volume = {161}, year = {2013}, }
TY - JOUR AU - Rimer Zurita TI - Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz JO - Acta Arithmetica PY - 2013 VL - 161 IS - 1 SP - 69 EP - 100 LA - fre KW - divisor problems; Rényi problem; Piltz function; Lindelöf hypothesis UR - http://eudml.org/doc/278958 ER -