Armand Borel

Automorphic Forms on Sl2 (R)

Herausgeber: Bollobas, Bela; Fulton, W.

• Gebundenes Buch

Produktbeschreibung

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 ^D*G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on ^D*G\G and its relationship with the classical automorphic forms on X, Poincaré series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2(^D*G/G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 208
• Erscheinungstermin: 5. Juni 2004
• Englisch
• Abmessung: 235mm x 157mm x 17mm
• Gewicht: 496g
• ISBN-13: 9780521580496
• ISBN-10: 0521580498
• Artikelnr.: 21479372

Inhaltsangabe

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.