Sur les moments d'une fonction additive

Adolph Hildebrand

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 3, page 1-22
  • ISSN: 0373-0956

Abstract

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We give precise estimations for the quantities 1 X ∑ n ≤ X | f ( n ) - A | β , where f is an additive arithmetical function and A , β > 0 and x ≥ 1 are real numbers.

How to cite

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Hildebrand, Adolph. "Sur les moments d'une fonction additive." Annales de l'institut Fourier 33.3 (1983): 1-22. <http://eudml.org/doc/74595>.

@article{Hildebrand1983,
abstract = {On donne des estimations précises pour les quantités $\{1\over X\}\sum _\{n\le X\}\vert f(n)-A\vert ^\beta $, où $f$ est une fonction arithmétique additive et $A,\beta &gt;0$ et $x\ge 1$ sont des nombres réels.},
author = {Hildebrand, Adolph},
journal = {Annales de l'institut Fourier},
keywords = {additive functions; Turan-Kubilius inequality; moments},
language = {fre},
number = {3},
pages = {1-22},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur les moments d'une fonction additive},
url = {http://eudml.org/doc/74595},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Hildebrand, Adolph
TI - Sur les moments d'une fonction additive
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 3
SP - 1
EP - 22
AB - On donne des estimations précises pour les quantités ${1\over X}\sum _{n\le X}\vert f(n)-A\vert ^\beta $, où $f$ est une fonction arithmétique additive et $A,\beta &gt;0$ et $x\ge 1$ sont des nombres réels.
LA - fre
KW - additive functions; Turan-Kubilius inequality; moments
UR - http://eudml.org/doc/74595
ER -

References

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  1. [1] P.D.T.A. ELLIOTT, High power analogues of the Turán-Kubilius inequality and an application to number theory, Can. J. Math., 32 (1980), 893-907. Zbl0444.10051MR81m:10082
  2. [2] P.D.T.A. ELLIOTT, Probabilistic number theory I, Springer, New York - Heidelberg - Berlin, 1979. Zbl0431.10029MR82h:10002a
  3. [3] P. ERDÖS et I.Z. RUZSA, On the small sieve I, J. Number Th., 12 (1980), 385-394. Zbl0435.10028
  4. [4] A. HILDEBRAND et J. SPILKER, Eine Charakterisierung der additiven, fastgeraden Funktionen, Manuscripta Math., 32 (1980), 213-230. Zbl0446.10041MR82g:10066
  5. [5] I.Z. RUZSA, On the concentration of additive functions, Acta Math. Acad. Sci. Hung., 36 (1980), 215-232. Zbl0471.10034MR82j:10088
  6. [6] I.Z. RUZSA, On the variance of additive functions, Preprint. Zbl0519.10045
  7. [7] I.Z. RUZSA, Generalized moments of additive functions, Preprint. Zbl0524.10042
  8. [8] D. WOLKE, Das Selbergsche Sieb für Zahlenthetische Funktionen I, Arch. Math., 24 (1973), 632-639. Zbl0278.10041MR49 #2618

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