Mathematics > Number Theory
[Submitted on 17 Jun 2024
]
Title: Vanishing of Poincaré series for congruence subgroups
Title: Poincaré 系列在同余子群中的消失
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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