Remarques sur les moyennes des fonctions de Piltz sur les entiers friables
Résumé
We study the mean value of generalized divisor functions $\tau_\kappa(n)$ over integers without large prime factors (here $\kappa>0$). We relate this problem to the computation of the ratio $\Psi(x^{1/\kappa}, y)^\kappa/\Psi(x, y)$ , involving the y-smooth numbers counting function. We establish an inverse theorem, giving limitations on the range in $(x,y)$ in which this ratio can be asymptotically estimated uniformly in $\kappa$.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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