This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Aron, Richard M.Bayart, FrédéricGauthier, Paul M.Maestre, ManuelNestoridis, Vassili2019-06-2820161864-7596https://doi.org/10.34657/2228https://oa.tib.eu/renate/handle/123456789/3133We characterize the uniform limits of Dirichlet polynomials on a right half plane. We extend the approximation theorems of Runge,Mergelyan and Vitushkin to the Dirichlet setting with respect to the Euclidean distance and to the chordal one, as well. We also strengthen the notion of Universal Dirichlet series.application/pdfeng510Universal seriesRunge theoremReport