Ebook: Quantization and Non-holomorphic Modular Forms

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).

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A manuscript bringing together quantization theory and the theory of non-holomorphic modular forms. Written especially for two kinds of readers, with recommendations for each type, the reader with an interest in modular form theory and the reader quantization theory and the other subjects covered by the monograph. Softcover.