Sur un problème de Rényi et Ivić concernant les fonctions de diviseurs de Piltz

Rimer Zurita

Acta Arithmetica (2013)

  • Volume: 161, Issue: 1, page 69-100
  • ISSN: 0065-1036

Abstract

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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 .

How to cite

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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 -

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