Metrisierungstheorie und Jacobiformen. (Metrization theory and Jacobi forms) (Q1821141)

The paper offers a new access to the metrization theory of Siegel modular forms. For any type to expand modular forms it is shown, how to find Poincaré series of specific importance in metrization theory. The known kinds of Poincaré series can be subordinated, thereby simplifying former proofs considerably. To show the efficiency, the method is applied to Fourier-Jacobi expansions. It is proved that there exist Poincaré series attached to Jacobi forms, which satisfy the main theorems of metrization theory.