Quantization and non-holomorphic modular forms / André Unterberger

Auteur: Unterberger, Andre (1940-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1742Langue: anglaisÉditeur: Berlin : Springer, 2000 ISBN: 9783540678618 ISSN: 1617-9692Note: ... One of the main goals of this monograph is to generalize the Rankin-Cohen brackets of modular forms to the case of non-holomorphic automorphic forms. In fact, the author envisions the non-holomorphic analogue of Rankin-Cohen brackets as a machine for producing Maass cusp forms. In the process of constructing the bilinear products, which generalize the Rankin-Cohen brackets, the author uses various techniques from pseudodifferential analysis, partial differential equations, and harmonic analysis such as the Radon transform, the Rankin-Selberg unfolding method, Weyl symbols, and Poisson brackets. In addition he discusses connections of such bilinear products with quantization theory. (Zentralblatt) Sujets MSC: 11F11 Number theory -- Discontinuous groups and automorphic forms -- Holomorphic modular forms of integral weight
11F25 Number theory -- Discontinuous groups and automorphic forms -- Hecke-Petersson operators, differential operators (one variable)
11L05 Number theory -- Exponential sums and character sums -- Gauss and Kloosterman sums; generalizations
81Sxx Quantum theory -- General quantum mechanics and problems of quantization
44A12 Integral transforms, operational calculus -- Integral transforms, operational calculus -- Radon transform
En-ligne: Springerlink | Zentralblatt | MathSciNet

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... One of the main goals of this monograph is to generalize the Rankin-Cohen brackets of modular forms to the case of non-holomorphic automorphic forms. In fact, the author envisions the non-holomorphic analogue of Rankin-Cohen brackets as a machine for producing Maass cusp forms. In the process of constructing the bilinear products, which generalize the Rankin-Cohen brackets, the author uses various techniques from pseudodifferential analysis, partial differential equations, and harmonic analysis such as the Radon transform, the Rankin-Selberg unfolding method, Weyl symbols, and Poisson brackets. In addition he discusses connections of such bilinear products with quantization theory. (Zentralblatt)

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