Vanishing of Poincar\'e series for congruence subgroups

Noam Kimmel

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arXiv · 2406.11302

Vanishing of Poincar\'e series for congruence subgroups

Noam Kimmel

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Abstract

We consider the problem of the vanishing of Poincar\'e series for congruence subgroups. Denoting by $P_{k,m,N}$ the Poincar\'e series of weight $k$ and index $m$ for the group $\Gamma_0(N)$, we show that for certain choices of parameters $k,m,N$, the Poincar\'e series does not vanish. Our methods improve on previous results of Rankin (1980) and Mozzochi (1989).

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Noam Kimmel. 2024-06-17. Vanishing of Poincar\'e series for congruence subgroups. https://arxiv.org/abs/2406.11302

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