Effective Erdős-Wintner theorems

Gérald Tenenbaum (1) , Johann Verwee (1)

1 IECL - Institut Élie Cartan de Lorraine

The classical theorem of Erdős & Wintner furnishes a criterion for the existence of a limiting distribution for a real, additive arithmetical function. This work is devoted to providing an effective estimate for the remainder term under the assumption that the conditions in the criterion are fulfilled. We also investigate the case of a conditional distribution.

Mots clés: distribution of real additive functions; mean values of complex multiplicative function; Erdős-Wintner theorem; effective averages; number of prime factors

Domaines: Théorie des nombres [math.NT]

Gérald Tenenbaum, Johann Verwee. Effective Erdős-Wintner theorems. Proceedings of the Steklov Institute of Mathematics, In press, ⟨10.1134/S008154382104012X⟩. ⟨hal-02950325⟩