Séries trigonométriques à coefficients arithmétiques

Régis de La Bretèche (1) , Gérald Tenenbaum (2)

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

By exploiting the recent analytic tool of friable summation, this work describes a new approach to a class of problems in multiplicative number theory and Fourier series theory originated by H. Davenport. A definite answer to the last original question of Davenport of this type, which was still open, as well as a number of other applications, is given.

Mots clés: largest prime factor; Fourier series; Gibbs phenomenon; friable integers; multiplicative functions; largest prime factor.

Domaines: Théorie des nombres [math.NT]

Régis de La Bretèche, Gérald Tenenbaum. Séries trigonométriques à coefficients arithmétiques. Journal d'analyse mathématique, 2004, 92, pp.1-79. ⟨hal-00145883⟩