Entiers friables: inégalité de Turán-Kubilius et applications

R. de La Bretèche (1) , Gérald Tenenbaum (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 IECN - Institut Élie Cartan de Nancy

We generalize the classical Turán-Kubilus inequality to friable integers and obtain sharp estimates for the involved constant in large subdomains. Several applications are derived in probabilitic number theory.

Mots clés: Turán-Kubilius inequality; friable numbers; Daboussi theorem; Erdös-Wintner theorem; Lévy distance; Kubilius model; Exponential sums

Domaines: Théorie des nombres [math.NT]

R. de La Bretèche, Gérald Tenenbaum. Entiers friables: inégalité de Turán-Kubilius et applications. Inventiones Mathematicae, 2005, 159 fasc. 3, pp.531-588. ⟨hal-00022451v3⟩