Composition operators on weighted Bergman spaces of Dirichlet series

We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some speci c cases, upper and lower bounds of the essential norm of these operators and a criterion of compactness on classicals weighted Bergman spaces. Moreover, a su cient condition of compactness is obtained using the notion of Carleson's measure.