Automorphic forms on SL₂(R)
This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this...
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| Format: | eBook |
| Language: | English |
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Cambridge
Cambridge University Press
1997
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| Series: | Cambridge tracts in mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Cambridge Books Online - Collection details see MPG.ReNa |
Table of Contents:
- Part I. Basic Material On SL2(R), Discrete Subgroups and the Upper-Half Plane:
- 1. Prerequisites and notation
- 2. Review of SL2(R), differential operators, convolution
- 3. Action of G on X, discrete subgroups of G, fundamental domains
- 4. The unit disc model
- Part II. Automorphic Forms and Cusp Forms:
- 5. Growth conditions, automorphic forms
- 6. Poincare series
- 7. Constant term:the fundamental estimate
- 8. Finite dimensionality of the space of automorphic forms of a given type
- 9. Convolution operators on cuspidal functions
- Part III. Eisenstein Series:
- 10. Definition and convergence of Eisenstein series
- 11. Analytic continuation of the Eisenstein series
- 12. Eisenstein series and automorphic forms orthogonal to cusp forms
- Part IV. Spectral Decomposition and Representations:
- 13. Spectral decomposition of L2(G\G)m with respect to C
- 14. Generalities on representations of G
- 15. Representations of SL2(R)
- 16. Spectral decomposition of L2(G\SL2(R)): the discrete spectrum
- 17. Spectral decomposition of L2(G\SL2(R)): the continuous spectrum
- 18. Concluding remarks