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

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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

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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 -

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