Plus grand facteur premier de valeurs de polynômes aux entiers
Volume 169 / 2015
Acta Arithmetica 169 (2015), 221-250
MSC: Primary 11N32.
DOI: 10.4064/aa169-3-2
Abstract
Let 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 \varPhi with integral coefficients and the associated Galois group isomorphic to V_4, there exists a positive constant c_\varPhi such that the set of integers n\leq X satisfying P^+ ( \varPhi (n) )\geq X^{1+c_\varPhi } has a positive density. Such a result was recently proved by Dartyge for \varPhi (n)=n^4-n^2+1. There is an appendix written with Jean-François Mestre.