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.

中文翻译：

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向量值庞加莱级数的不消失

我们证明了上半平面上庞加莱级数的Muić积分不消失准则的向量值版本 $\mathcal{H}$。此外，我们给出了庞加莱级数形式的向量值模块化形式的构造的伴随结果。作为这些结果的应用，我们构造和研究了经典和椭圆向量值庞加莱级数的不消失性。