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Pré-Publication, Document De Travail Année : 2007

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 $L(1, \chi)$.
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Dates et versions

hal-02572687 , version 1 (13-05-2020)

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  • HAL Id : hal-02572687 , version 1

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Olivier Ramaré. Tame behaviour of the mean value of multiplicative functions and some inequalities relating values of Dirichlet series. 2007. ⟨hal-02572687⟩
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