Quantum ergodicity for Eisenstein series at complex energies

Quantum ergodicity concerns the structure of measures arising from high energy quantum objects. We consider the case of Eisenstein series for surfaces with cusps at complex energies located a fixed distance away from the real axis. For such objects, the limiting measures are rigid without any dependence on finer aspects of the flow in the compact part. In particular, resonant states at such energies also converge to a finite dimensional space of possible measures (and a fixed measure if there is only one cusp).