Remarques sur les valeurs moyennes de fonctions multiplicatives

Gérald Tenenbaum (1)

1 IECN - Institut Élie Cartan de Nancy

By a self-contained approach, we show that a real valued multiplicative function whose square has a mean-value must itself have a mean value, and we provide a sufficient condition for the vanishing of the latter. This partially extends a theorem of Elliott.

Mots clés: Mean values of multiplicative functions; Tauberian theorems

Domaines: Théorie des nombres [math.NT]

Gérald Tenenbaum. Remarques sur les valeurs moyennes de fonctions multiplicatives. L'Enseignement Mathématique , 2007, (2) 53, pp.155-178. ⟨hal-00131535v3⟩