| Preface |
| Lectures on L-functions, Converse Theorems, and Functoriality for GL(n) / James W. Cogdell |
| Modular Forms and Their L-functions / Lecture 1.： |
| Examples / 1.： |
| Growth estimates on cusp forms / 2.： |
| The L-function of a cusp form / 3.： |
| The Euler product / 4.： |
| References / 5.： |
| Automorphic Forms / Lecture 2.： |
| Automorphic forms on GL[subscript 2] |
| Automorphic forms on GL[subscript n] |
| Smooth automorphic forms |
| L[superscript 2]-automorphic forms |
| Cusp forms |
| Automorphic Representations / 6.： |
| (K-finite) automorphic representations |
| Smooth automorphic representations |
| L[superscript 2]-automorphic representations |
| Cuspidal representations |
| Connections with classical forms |
| Fourier Expansions and Multiplicity One Theorems / Lecture 4.： |
| The Fourier expansion of a cusp form |
| Whittaker models |
| Multiplicity one for GL[subscript n] |
| Strong multiplicity ones for GL[subscript n] |
| Eulerian Integral Representations / Lecture 5.： |
| GL[subscript 2] x GL[subscript 1] |
| GL[subscript n] x GL[subscript m] with m [less than sign] n |
| GL[subscript n] x GL[subscript n] |
| Summary |
| Local L-functions: The Non-Archimedean Case / Lecture 6.： |
| Whittaker functions |
| The local L-function (m [less than sign] n) |
| The local functional equation |
| The conductor of [pi] |
| Multiplicativity and stability of [gamma]-factors |
| The Unramified Calculation / Lecture 7.： |
| Unramified representations |
| Unramified Whittaker functions |
| Calculating the integral |
| Local L-functions: The Archimedean Case / Lecture 8.： |
| The arithmetic Langlands classification |
| The L-functions |
| The integrals (m [less than sign] n) |
| Is the L-factor correct? |
| Global L-functions / Lecture 9.： |
| Convergence |
| Meromorphic continuation |
| Poles of L-functions |
| The global functional equation |
| Boundedness in vertical strips |
| Strong Multiplicity One revisited / 7.： |
| Generalized Strong Multiplicity One / 8.： |
| Converse Theorems / 9.： |
| Converse Theorems for GL[subscript n] |
| Inverting the integral representation |
| Proof of Theorem 10.1 (i) |
| Proof of Theorem 10.1 (ii) |
| Theorem 10.2 and beyond |
| A useful variant |
| Conjectures |
| Functoriality / Lecture 11.： |
| The Weil-Deligne group |
| The dual group |
| The local Langlands conjecture |
| Local functoriality |
| Global functoriality |
| Functoriality and the Converse Theorem |
| Functoriality for the Classical Groups / Lecture 12.： |
| The results |
| Construction of a candidate lift |
| Analytic properties of L-functions |
| Apply the Converse Theorem |
| Functoriality for the Classical Groups, II / Lecture 13.： |
| Descent |
| Bounds towards Ramanujan |
| The local converse theorem |
| Further applications |
| Automorphic L-functions / Henry H. Kim |
| Introduction |
| Chevalley Groups and their Properties / Chapter 1.： |
| Algebraic groups |
| Roots and coroots |
| Classification of root systems |
| Construction of Chevalley groups: simply connected type |
| Structure of parabolic subgroups |
| Cuspidal Representations / Chapter 2.： |
| L-groups and Automorphic L-functions / Chapter 3.： |
| Induced Representations / Chapter 4.： |
| Harish-Chandra homomorphisms |
| Induced representations: F local |
| Intertwining operators for I(s, [pi]) |
| Digression on admissible representations |
| Induced representations: F global |
| Induced representations as holomorphic fiber bundles |
| Eisenstein Series and Constant Terms / Chapter 5.： |
| Definition of Eisenstein series |
| Constant terms |
| Psuedo-Eisenstein series |
| L-functions in the Constant Terms / Chapter 6.： |
| List of L-functions via Langlands-Shahidi method |
| Meromorphic Continuation of L-functions / Chapter 7.： |
| Generic Representations and their Whittaker Models / Chapter 8.： |
| General case |
| Whittaker models for induced representations |
| Local Coefficients and Non-constant Terms / Chapter 9.： |
| Non-constant terms of Eisenstein series |
| Local coefficients and crude functional equation |
| Local Langlands Correspondence / Chapter 10.： |
| Local L-functions and Functional Equations / Chapter 11.： |
| Definition of local L-functions |
| Properties of local L-functions; supercuspidal representations |
| Normalization of Intertwining Operators / Chapter 12.： |
| [pi] is supercuspidal |
| [pi] is tempered, generic |
| [pi] is non-tempered, generic |
| Application to reducibility criterion |
| Holomorphy and Bounded in Vertical Strips / Chapter 13.： |
| Holomorphy of L-functions |
| Boundedness in vertical strips of L-functions |
| Langlands Functoriality Conjecture / Chapter 14.： |
| Converse Theorem of Cogdell and Piatetski-Shapiro / Chapter 15.： |
| Functoriality of the Symmetric Cube / Chapter 16.： |
| Weak Ramanujan property |
| Functoriality of the symmetric square |
| Functoriality of the tensor product of GL[subscript 2] x GL[subscript 3] |
| Functoriality of the symmetric cube |
| Functoriality of the Symmetric Fourth / Chapter 17.： |
| Functoriality of the exterior square |
| Functoriality of the symmetric fourth |
| Bibliography |
| Applications of Symmetric Power L-functions / M. Ram Murty |
| The Sato-Tate Conjecture |
| Uniform distribution |
| Wiener-Ikehara Tauberian theorem |
| Weyl's theorem for compact groups |
| Maass Wave Forms |
| Maass forms of weight zero |
| Maass forms with weight |
| Eisenstein series |
| Upper bound for Fourier coefficients and eigenvalue estimators |
| The Rankin-Selberg Method |
| Eisenstein series and non-vanishing of [xi](s) on R(s) = 1 |
| Explicit construction of Maass cusp forms |
| The Rankin-Selberg L-function |
| Rankin-Selberg L-functions for GL[subscript n] |
| Oscillations of Fourier Coefficients of Cusp Forms |
| Preliminaries |
| Rankin's theorem |
| A review of symmetric power L-functions |
| Proof of Theorem 4.1 |
| Poincare Series |
| Poincare series for SL[subscript 2] (Z) |
| Fourier coefficients and Kloosterman sums |
| The Kloosterman-Selberg zeta function |
| Kloosterman Sums and Selberg's Conjecture |
| Petersson's formula |
| Selberg's theorem |
| The Selberg-Linnik conjecture |
| Refined Estimates for Fourier Coefficients of Cusp Forms |
| Sieve theory and Kloosterman sums |
| Gauss sums and hyper-Kloosterman sum |
| The Duke-Iwaniec method |
| Twisting and Averaging of L-series |
| Selberg conjectures for GL[subscript n] |
| Ramanujan conjecture for Gl[subscript n] |
| The method of averaging L-functions |
| The Kim-Sarnak Theorem |
| Rankin-Selberg theory |
| An application of the Duke-Iwaniec method |
| Introduction to Artin L-functions |
| Hecke L-functions |
| Artin L-functions |
| Automorphic induction and Artin's conjecture |
| Zeros and Poles of Artin L-functions |
| The Heilbronn character |
| The fundamental inequality |
| Rankin-Selberg property for Galois representations |
| The Langlands-Tunnell Theorem |
| Review of some group theory |
| Some representation theory |
| An application of the Deligne-Serre theory |
| The general case |
| Sarnak's theorem |
| Preface |
| Lectures on L-functions, Converse Theorems, and Functoriality for GL(n) / James W. Cogdell |
| Modular Forms and Their L-functions / Lecture 1.： |
図書
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