Convergence of Poincare series on Hecke groups of large width

Abstract

In earlier work, we described a relation between the parameters associated with multiplier systems of complex weight on the discrete Hecke groups $G_{\lambda }$ when $1 \leq \lambda \lt 2$, and consequently showed that parabolic Poincare series of nonreal weight on the modular group are not absolutely convergent anywhere. In the current paper we establish an analogous divergence result for all Hecke groups with $\lambda > 2$.