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Deux remarques sur les séries et les polynômes de Dirichlet

Christian Deutsch — 1974

Annales de l'institut Fourier

Cette note contient deux résultats : - d’une part, une majoration de l’abscisse d’absolue convergence du développement en série de Dirichlet de l’inverse de la somme d’une série de Dirichlet donnée. - d’autre part, le fait que tout polynôme de Dirichlet non constant $1 + \sum_{2 \leq k \leq N} a_{k} λ_{k}^{- s} où les a_{k} sont des entiers relatifs$ et les $λ_{k}$ sont des nombres réels $> 1$ s’annule dans tout demi-plan Réel $s > - ϵ$ où $ϵ > 0$ . L’un et l’autre de ces résultats sont conséquences d’une proposition que l’on démontre en utilisant...

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