Hecke-Integrale mit rationalen periodischen Funktionen und Dirichlet-Reihen mit Funktionalgleichung

A Hecke correspondence theorem for automorphic integrals with symmetric rational period functions on the Hecke groups

“…Choie and Zagier [1] and Parson [16] gave an explicit characterization of RPFs on the modular group that made possible the correspondence in [4]. The problem of finding a characterization of RPFs on all of the Hecke groups remains open, although several authors have done work in this direction [5,17,19,22,23]. These results provide enough information about the structure of RPFs on the Hecke groups for us to prove our correspondence theorem.…”

“…The problem of finding a characterization of RPFs on all of the Hecke groups remains open, although several authors have done work in this direction [3,10,12,15,16]. These results provide enough information about the structure of RPFs on the Hecke groups for us to prove a correspondence theorem for modular integrals with certain rational period functions.…”

“…Meier and Rosenberger [10] observed that all the poles of q are real, and showed that if q has a pole only at zero it must be of the form…”

“…Suppose that F (z) is an entire automorphic integral of weight 2k on G p with Hecke-symmetric rational period function q(z) given by (7). Suppose that F has the Fourier expansion (1) with zero constant term, and that Φ(s) is given by (10) for Re(s) > β, for some positive β.…”

On Binary Quadratic Forms and the Hecke Groups

“…Let c k = sin(kπ/p) sin(π/p) for k ≥ 0. Meier and Rosenberger [4] show that as linear fractional transformations…”