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(GG)m with respect to C; 14. Generalities on representations of G; 15. Representations of SL2(R); 16. Spectral decomposition of L2(GSL2(R)):the discrete spectrum; 17. Spectral decomposition of L2(GSL2(R)): the continuous spectrum; 18. Concluding remarks.

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An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.

Reviews

From the hardback review: 'This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.' Victor Snaith, Bulletin of the London Mathematical Society From the hardback review: '... carefully and concisely written ... Clearly every mathematical library should have this book.' Zentralblatt