Cover......Page 1
Series Page......Page 3
Eisenstein Series andAutomorphic Representationswith Applications in String Theory......Page 5
Copyright......Page 6
Dedications......Page 7
Contents......Page 9
List of Definitions and Theorems......Page 13
List of Examples......Page 16
Preface......Page 19
1 Motivation and Background......Page 21
PART ONE: AUTOMORPHIC REPRESENTATIONS......Page 37
2 Preliminaries on p-adic and Adelic Technology......Page 39
3 Basic Notions from Lie Algebras and Lie Groups......Page 59
4 Automorphic Forms......Page 78
5 Automorphic Representations and Eisenstein Series......Page 107
6 Whittaker Functions and Fourier Coefficients......Page 143
7 Fourier Coefficients of Eisenstein Series on SL(2,��)......Page 175
8 Langlands Constant Term Formula......Page 190
9 Whittaker Coefficients of Eisenstein Series......Page 206
10 Analysing Eisenstein Series and Small Representations......Page 239
11 Hecke Theory and Automorphic L-functions......Page 275
12 Theta Correspondences......Page 310
PART TWO: APPLICATIONS IN STRING THEORY......Page 325
13 Elements of String Theory......Page 327
14 Automorphic Scattering Amplitudes......Page 387
15 Further Occurrences ofAutomorphic Forms in String Theory......Page 415
PART THREE: ADVANCED TOPICS......Page 449
16 Connections to the Langlands Program......Page 451
17 Whittaker Functions, Crystals and Multiple Dirichlet Series......Page 471
18 Automorphic Forms on Non-split Real Forms......Page 480
19 Extension to KacβMoody Groups......Page 507
APPENDICES......Page 527
Appendix A: SL(2, β) Eisenstein Series and PoissonResummation......Page 529
Appendix B: Laplace Operators on G/K and Automorphic Forms......Page 533
Appendix C: Structure Theory of ����(2, 1)......Page 538
Appendix D: PoincarΓ© Series and Kloosterman Sums......Page 541
References......Page 547
Index......Page 579