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Séries de Dirichlet à deux variables et distribution des valeurs de fonctions arithmétiques.

Abstract : We deal with two problems related to Dirichlet series. First we study the analytic continuation of a class of Dirichlet series with two variables : g(s_1,s_2,a,r)=∑ (d≥1) r(d)a(d)^{-s_1}d^{-s_2}, where a(d) is a positive multiplicative function and r(d) is a multiplicative function. We prove, under certain hypotheses, a general theorem which allows us to approach this Dirichlet series by a known series, modulo another series for which we get very precise upper bounds. Then we use this tool to get quantitative results on the distribution of values of arithmetical functions. Under certain hypotheses on the functions a(d) and r(d), we determine X^{-1}∑ (d≤X, a(d)≤z) r(d) (0
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https://tel.archives-ouvertes.fr/tel-00426287
Contributor : Amandine Saldana <>
Submitted on : Friday, October 23, 2009 - 11:15:09 PM
Last modification on : Sunday, November 29, 2020 - 3:24:09 AM
Long-term archiving on: : Tuesday, October 16, 2012 - 12:40:09 PM

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Saldana Amandine. Séries de Dirichlet à deux variables et distribution des valeurs de fonctions arithmétiques.. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2009. Français. ⟨tel-00426287⟩

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