Estimation de sommes multiples de fonctions arithmétiques

Régis de la Bretèche

doi:10.1023/A:1011803816545

Abstract

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We estimate some sums of the shape S(Xβ1,…, Xβm): = [sum ]1 [les ] d1 [les ] Xβ1… [sum ]1 [les ] dm [les ] Xβm ƒ(d1,…, dm), when m ∈ $\Bbb N$ and f is a nonnegative arithmetical function. We relate them to the behaviour of the associated Dirichlet series

F(s1,…, sm) = ∞[sum ]d1 = 1 … ∞[sum ]dm = 1 f(d1,…, dm)/d1s1 … dmsm. The main aim of this work is to develop analytic tools to count the rational points of bounded height on toric varieties.

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Estimation de sommes multiples de fonctions arithmétiques

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Estimation de sommes multiples de fonctions arithmétiques

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