Non-vanishing of vector-valued Poincaré series

Abstract

We prove a vector-valued version of Muić's integral non-vanishing criterion for Poincaré series on the upper half-plane $\mathcal{H}$. Moreover, we give an accompanying result on the construction of vector-valued modular forms in the form of Poincaré series. As an application of these results, we construct and study the non-vanishing of the classical and elliptic vector-valued Poincaré series.

22 pages