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Quantization and non-holomorphic modular forms
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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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Quantization and non-holomorphic modular forms, Andre Unterberger
- Language
- Released
- 2000
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- Title
- Quantization and non-holomorphic modular forms
- Language
- English
- Authors
- Andre Unterberger
- Publisher
- Springer
- Released
- 2000
- ISBN10
- 3540678611
- ISBN13
- 9783540678618
- Series
- Lecture notes in mathematics
- Category
- Mathematics
- 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).