This is a new approach to the theory of non-holomorphic modular forms,
based on ideas from quantization theory or pseudodifferential analysis.
Extending the Rankin-Selberg method so as to apply it to the calculation
of the Roelcke-Selberg decomposition of the product of two Eisenstein
series, one lets Maass cusp-forms appear as residues of simple,
Eisenstein-like, series. Other results, based on quantization theory,
include a reinterpretation of the Lax-Phillips scattering theory for the
automorphic wave equation, in terms of distributions on R2 automorphic
with respect to the linear action of SL(2, Z).