Un crible minorant effectif pour les entiers friables

Let A be a finite set of positive integers and let y≥1. We give an effective lower bound of the cardinality of the set {n∈A:p|n⇒p≤y} under the condition of a good knowledge of the level of distribution of A. Some consequences are studied: an application to the friable values of irreducible polynomials or binary forms with integer coefficients, and an application to shifted friable numbers.