English

Vanishing of Poincar\'e series for congruence subgroups

Number Theory 2024-06-18 v1

Abstract

We consider the problem of the vanishing of Poincar\'e series for congruence subgroups. Denoting by Pk,m,NP_{k,m,N} the Poincar\'e series of weight kk and index mm for the group Γ0(N)\Gamma_0(N), we show that for certain choices of parameters k,m,Nk,m,N, the Poincar\'e series does not vanish. Our methods improve on previous results of Rankin (1980) and Mozzochi (1989).

Keywords

Cite

@article{arxiv.2406.11302,
  title  = {Vanishing of Poincar\'e series for congruence subgroups},
  author = {Noam Kimmel},
  journal= {arXiv preprint arXiv:2406.11302},
  year   = {2024}
}