Propriétés multiplicatives des entiers friables translatés

Sary Drappeau

Colloquium Mathematicae (2014)

  • Volume: 137, Issue: 2, page 149-164
  • ISSN: 0010-1354

Abstract

top
An integer n is said to be y-friable if its greatest prime factor P(n) is less than y. In this paper, we study numbers of the shape n-1 when P(n) ≤ y and n ≤ x. One expects that, statistically, their multiplicative behaviour resembles that of all integers less than x. Extending a result of Basquin (2010), we estimate the mean value over shifted friable numbers of certain arithmetic functions when ( l o g x c ) ≤ y for some positive c, showing a change in behaviour according to whether log y/log x tends to infinity or not. In the same range in (x, y), we prove an Erdős-Kac-type theorem for shifted friable numbers, improving a result of Fouvry Tenenbaum (1996). The results presented here are obtained using recent work of Harper (2012) on the statistical distribution of friable numbers in arithmetic progressions.

How to cite

top

Sary Drappeau. "Propriétés multiplicatives des entiers friables translatés." Colloquium Mathematicae 137.2 (2014): 149-164. <http://eudml.org/doc/284124>.

@article{SaryDrappeau2014,
author = {Sary Drappeau},
journal = {Colloquium Mathematicae},
language = {fre},
number = {2},
pages = {149-164},
title = {Propriétés multiplicatives des entiers friables translatés},
url = {http://eudml.org/doc/284124},
volume = {137},
year = {2014},
}

TY - JOUR
AU - Sary Drappeau
TI - Propriétés multiplicatives des entiers friables translatés
JO - Colloquium Mathematicae
PY - 2014
VL - 137
IS - 2
SP - 149
EP - 164
LA - fre
UR - http://eudml.org/doc/284124
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.