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 d k ( n ) 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 ∑ n ≤ x , Ω ( n ) - ω ( n ) = q f ( n ) for a class of multiplicative functions f, including in particular f ( n ) = d k ( n ) , 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 f ( n ) = σ r ( n ) / ( n r ) (where σ r 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 f ( n ) = d 2 ( n ) .

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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