Quantization and Non-holomorphic Modular Forms
(Sprache: Englisch)
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...
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Klappentext zu „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).
Inhaltsverzeichnis zu „Quantization and Non-holomorphic Modular Forms “
- Introduction- Distributions associated with the non-unitary principal series
- Modular distribution
- The principal series of SL(2,R) and the Radon transform
- Another look at the composition of Weyl symbols
- The Roelcke-Selberg decomposition and the Radon transform
- Recovering the Roelcke-Selberg coefficients of a function in L2 of the fundamental domain
- The "product" of two Eisenstein distributions
- The Roelcke-Selberg expansion of the product of two Eisenstein series : the continuous part
- A digression on Kloosterman sums
- The Roelcke-Selberg expansion of the product of two Eisenstein series : the discrete part
- The expansion of the Poisson bracket of two Eisenstein series
- Automorphic distributions on R2
- The Hecke decomposition of products or Poisson brackets of two Eisenstein series
- A generating series of sorts for Maass cusp-forms
- Some arithmetic distributions
- Quantization, products and Poisson Brackets
- Moving to the forward light-cone: the Lax-Phillips theory revisited ...
Bibliographische Angaben
- Autor: André Unterberger
- 2000, 268 Seiten, Maße: 15,5 x 23,3 cm, Kartoniert (TB), Englisch
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3540678611
- ISBN-13: 9783540678618
- Erscheinungsdatum: 28.08.2000
Sprache:
Englisch
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