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arXiv · 2007.16159

Non-vanishing of vector-valued Poincar\'e series

Sonja Žunar
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Abstract

We prove a vector-valued version of Mui\'c's integral non-vanishing criterion for Poincar\'e 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 Poincar\'e series. As an application of these results, we construct and study the non-vanishing of the classical and elliptic vector-valued Poincar\'e series.

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Sonja Žunar. 2020-07-31. Non-vanishing of vector-valued Poincar\'e series. https://arxiv.org/abs/2007.16159

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