Quantization and non-holomorphic modular forms / André Unterberger
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1742Langue : anglais.Éditeur : Berlin : Springer, 2000ISBN: 9783540678618.ISSN: 1617-9692.Sujet MSC : 11F11, Discontinuous groups and automorphic forms, Holomorphic modular forms of integral weight11F25, 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, Radon transformEn-ligne : Springerlink | Zentralblatt | MathSciNet
... 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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