Weighted holomorphic Dirichlet series and composition operators with polynomial symbols

In this paper, we introduce a general class of weighted spaces holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. the particular case when symbol inducing operator is an affine function, give criteria for boundedness compactness. We also cyclicity property as byproduct characterization so that direct sum identity plus forward shift $\ell^2$ cyclic.