Title: Quantization and non-holomorphic modular forms
First published: 2000
Description: 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).
Subjects: Forms, Modular, Geometric quantization, Modular Forms, Quantification geometrique, Geometrische Quantisierung, Kwantummechanica, Formes modulaires, Vormen (wiskunde), Modulform, Mathematische fysica, Teoria dos numeros, Forms (mathematics), Mathematics, Number theory
LC classification: QA3 .L28 no. 1742, QC174.17.G46 .L28 no. 1742