Plus grand facteur premier de valeurs de polynômes aux entiers

R. de la Bretèche

Acta Arithmetica (2015)

  • Volume: 169, Issue: 3, page 221-250
  • ISSN: 0065-1036

Abstract

top
Let P⁺(n) denote the largest prime factor of the integer n. Using the Heath-Brown and Dartyge methods, we prove that for any even unitary irreducible quartic polynomial Φ with integral coefficients and the associated Galois group isomorphic to V₄, there exists a positive constant c Φ such that the set of integers n ≤ X satisfying P ⁺ ( Φ ( n ) ) ≥ X 1 + c Φ has a positive density. Such a result was recently proved by Dartyge for Φ(n) = n⁴ - n² + 1. There is an appendix written with Jean-François Mestre.

How to cite

top

R. de la Bretèche. "Plus grand facteur premier de valeurs de polynômes aux entiers." Acta Arithmetica 169.3 (2015): 221-250. <http://eudml.org/doc/279316>.

@article{R2015,
author = {R. de la Bretèche},
journal = {Acta Arithmetica},
language = {fre},
number = {3},
pages = {221-250},
title = {Plus grand facteur premier de valeurs de polynômes aux entiers},
url = {http://eudml.org/doc/279316},
volume = {169},
year = {2015},
}

TY - JOUR
AU - R. de la Bretèche
TI - Plus grand facteur premier de valeurs de polynômes aux entiers
JO - Acta Arithmetica
PY - 2015
VL - 169
IS - 3
SP - 221
EP - 250
LA - fre
UR - http://eudml.org/doc/279316
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.