Eisenstein Series and Automorphic Representations

1. Motivation and background
Part I. Automorphic Representations:
2. Preliminaries on p-adic and adelic technology
3. Basic notions from Lie algebras and Lie groups
4. Automorphic forms
5. Automorphic representations and Eisenstein series
6. Whittaker functions and Fourier coefficients
7. Fourier coefficients of Eisenstein series on SL(2, A)
8. Langlands constant term formula
9. Whittaker coefficients of Eisenstein series
10. Analysing Eisenstein series and small representations
11. Hecke theory and automorphic L-functions
12. Theta correspondences
Part II. Applications in String Theory:
13. Elements of string theory
14. Automorphic scattering amplitudes
15. Further occurrences of automorphic forms in string theory
Part III. Advanced Topics:
16. Connections to the Langlands program
17. Whittaker functions, crystals and multiple Dirichlet series
18. Automorphic forms on non-split real forms
19. Extension to Kac–Moody groups
Appendix A. SL(2, R) Eisenstein series and Poisson resummation
Appendix B. Laplace operators on G/K and automorphic forms
Appendix C. Structure theory of su(2, 1)
Appendix D. Poincaré series and Kloosterman sums
References
Index.