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In this paper, we introduce a general class of weighted spaces of holomorphicDirichlet series (with real frequencies) analytic in some half-plane and studycomposition operators on these spaces. In the particular case when the symbolinducing the composition operator is an affine function, we give criteria forboundedness and compactness. We also study the cyclicity property and as abyproduct give a sufficient condition so that the direct sum of the identityplus a weighted forward shift operator on the Hardy space H^2 is cyclic.

Weighted holomorphic Dirichlet series and composition operators with polynomial symbols