Sommes sans grand facteur premier
Plus grand facteur premier de valeurs de polynômes aux entiers
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 such that the set of integers n ≤ X satisfying 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.
Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes
Sums of arithmetic functions over values of binary forms
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