Plus grand facteur premier de valeurs de polynômes aux entiers

• Autorzy: R. de la Bretèche
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11N32: Primes represented by polynomials; other multiplicative structure of polynomial values

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 169
• Numer: 3
• Strony: 221-250

Daty

wydano

2015

Twórcy

autor

R. de la Bretèche

• Institut de Mathématiques de Jussieu, UMR 7586, Université Paris-Diderot, UFR de Mathématiques, case 7012, Bâtiment Sophie Germain, 75205 Paris Cedex 13, France

Identyfikatory

DOI

10.4064/aa169-3-2