On the uniform convergence of Poincaré series of exponential type on Jacobi groups
The author studies Jacobi forms on \({\mathcal H}_g\times\mathbb{C}^g\), where \({\mathcal H}_g\) is the Siegel half-space of genus \(g\). He derives absolute uniform convergence of Poincaré series of exponential type in vertical strips (where additionally the boundedness of the real parts in his theorem is required). The basic idea is to verify the Jacobi-Poincaré series essentially as a subseries of the Siegel-Poincaré series of exponential type on \({\mathcal H}_{g+1}\) and to use the known convergence behavior of this type.
scientific article; zbMATH DE number 977860