Tame behaviour of the mean value of multiplicative functions and some inequalities relating values of Dirichlet series
Résumé
We show that the average of a bounded multiplicative function varies locally in a regular manner. Our precise result improves on a similar one by Elliott. We use two novel ingredients: a better smoothing device, and a bilinear inequality for values of Dirichlet series. This last inequality leads to a refinement of a Theorem of Barrucand & Louboutin on lower bounds of $L(1, \chi)$.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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