Remarques sur les moyennes des fonctions de Piltz sur les entiers friables

Abstract : 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 $\kappa$.
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Sary Drappeau. Remarques sur les moyennes des fonctions de Piltz sur les entiers friables. Quarterly Journal of Mathematics, Oxford University Press (OUP), 2016, 67 (4), pp.507-517. ⟨10.1093/qmath/haw027⟩. ⟨hal-01476843⟩

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