June 17, 2024Open Access

Vanishing of Poincar\'e series for congruence subgroups

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Abstract

We consider the problem of the vanishing of Poincar\'e series for congruence subgroups. Denoting by P₊, ₌, ₍ the Poincar\'e series of weight k and index m for the group 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 (Mon,) studied this question.

synapsesocial.com/papers/68e64779b6db6435875d9031 https://doi.org/https://doi.org/10.48550/arxiv.2406.11302

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