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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).

Geometric quantization. --- Forms, Modular. --- Formes [Modulaires] --- Forms [Modular ] --- Geometric quantization --- Geometry (quantum) --- Quantization (geometric) --- Quantum geometry --- Vormen [Modulaire ] --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra

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Forms, Modular. --- Forms, Modular --- 511.334 --- Modular forms --- Modular and quadratic forms --- 511.334 Modular and quadratic forms --- Forms (Mathematics) --- Algebraic geometry --- Nombres, Théorie des --- Formes modulaires --- Number theory --- Nombres, Théorie des