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L-functions and Functoriality&James W.Cogdell 1

Ⅰ L-functions for GL(n)and Converse Theorems 3

1 Modular Forms and Automorphic Representations 3

2 L-functions for GLn and Converse Theorems 8

Ⅱ L-functions via Eisenstein Series 15

3 The Origins：Langlands 15

4 The Method：Langlands-Shahidi 21

5 The Results：Shahidi 26

Ⅲ Functoriality 30

6 Langlands Conjectures and Functoriality 30

7 The Converse Theorem and Functoriality 36

8 Symmetric Powers and Applications 41

References 47

Twisted Hilbert Modular L-functions and Spectral Theory&Gergely Harcos 49

1 Lecture One：Some Quadratic Forms 49

2 Lecture Two：More Quadratic Forms 53

3 Lecture Three：Preliminaries from Number Theory 56

4 Lecture Four：Subconvexity of Twisted L-functions 61

Acknowledgments 64

References 64

The Voronoi Formula for the Triple Divisor Function&Xiaoqing Li 69

1 Introduction 69

2 Proof of the Main Theorem 71

Acknowledgments 89

References 89

Linnik's Ergodic Method and the Hasse Principle for Ternary Quadratic Forms&Philippe Michel 91

1 Foreword 91

2 Integral Quadratic Forms 92

3 The Hasse Principle 93

4 Quadratic Forms over Lattices 96

5 Equidistribution on Adelic Quotient 101

6 Properties of the Adeles 106

7 The Hasse Integral Principle and Equidistribution of Adelic Orbits 114

8 The Ergodic Method 118

References 129

Automorphic Periods and Representation Theory&Andre Reznikov 131

1 Automorphic Representations and Frobenius Reciprocity 131

2 Bounds on Periods and Representation Theory 143

Acknowledgments 147

References 147

Eisenstein Series,L-functions and Representation Theory&Freydoon Shahidi 149

1 Preliminaries 150

2 L-Groups,L-Functions and Generic Representations 151

3 Eisenstein Series and Intertwining Operators;The Constant Term 154

4 Constant Term and Automorphic L-Functions 156

5 Examples 160

6 Local Coefficients,Nonconstant Term and the Crude Functional Equation 160

7 The Main Induction,Functional Equations and Multiplicativity 162

8 Twists by Highly Ramified Characters,Holomorphy and Boundedness 166

9 Examples of Functoriality with Applications 168

10 Applications to Representation Theory 171

References 173

Lecture Notes on Some Analytic Properties of Automorphic L-functions for SL2(Z)&Yangbo Ye 179

1 Introduction 179

2 An Integral Representation and Functional Equation 180

3 A Converse Theorem 188

4 The Phragmén-Lindel？f Principle and Convexity 193

5 The Rankin-Selberg Theory 197

References 202