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Here k is an arbitrary real number (the weight) and λ > 2, but otherwise unrestricted. The proof entails the use of the Riemann–Hecke–Bochner correspondence between modular integrals on the one side, and Dirichlet series with functional equations, on the other. It requires, as well, an application of Eichler’s generalized Poincare series. Since λ > 2 here, the underlying group of invariance, the Hecke triangle group

On Dirichlet series and Hecke triangle groups of infinite volume