自守形式与L-函数

L-functions and Functoriality

James W. Cogdell

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

1 Modular Forms and Automorphic Representations

2 L-functions for G/i and Converse Theorems

Ⅱ L-functions via Eisenstein Series

3 The Origins: Langlands

4 The Method: Langlands-Shahidi

5 The Results: Shahidi

Ⅲ Functoriality

6 Langlands Conjectures and Functoriality

7 The Converse Theorem and Functoriality

8 Symmetric Powers and Applications

References

Twisted Hilbert Modular L-functions and Spectral Theory

Gergely Harcos

1 Lecture One: Some Quadratic Forms

2 Lecture Two: More Quadratic Forms

3 Lecture Three: Preliminaries from Number Theory

4 Lecture Four: Subconvexity of Twisted /-functions

Acknowledgments

References

The Voronoi Formula for the rlyiple Divisor Function

Xiaoqin.g Li

1 Introduction

2 Proof of the Main Theorem

Acknowledgments

References

Linnik's Ergodic Method and the Hasse Principle for Ternary Quadratic Forms

Philippe Michel

1 Foreword

2 Integral Quadratic Forms

3 TheHassePrinciple

4 Quadratic Forms over Lattices

5 Equidistribution on Adelic Quotient

6 Properties of the Adeles

7 The Hasse Integral Principle and Equidistribution of Adelic Orbits

8 The Ergodic Method

References

Automorphic Periods and Representation Theory

Andre Reznikov

1 Automorphic Representations and Frobenius Reciprocity

2 Bounds on Periods and Representation Theory

Acknowledgments

References

Eisenstein Series, L-functions and Representation Theory Freydoon Shahidi

1 Preliminaries

2 L-Groups, L-Functions and Generic Representations

3 Eisenstein Series and Intertwining Operators; The Constant Term

4 Constant Term and Automorphic /-Functions

5 Examples

6 Local Coefficients, Nonconstant Term and the Crude Functional Equation

7 The Main Induction, Functional Equations and Multiplicativity

8 Twists by Highly Ramified Characters, Holomorphy and Boundedness

9 Examples of Functoriality with Applications

10 Applications to Representation Theory

References

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

Yangbo Ye

1 Introduction

2 An Integral Representation and Functional Equation

3 A Converse Theorem

4 The Phragmen-Lindelof Principle and Convexity

5 The Rankin-Selberg Theory

References

CIMPA-UNESCO-CHINA暑期学校“自守形式与L-函数”于2010年8月1日至14日在山东大学威海校区举办，该国际暑期学校受联合国教科文组织资助，邀请的演讲人都是本领域著名的专家。《自守形式与L-函数》汇集了这次暑期学校以下演讲人的讲义：J.Cogdell，G.Harcos，李小青，P.Michel，A.Reznikov，F.Shahidi以及叶扬波。《自守形式与L-函数》涵盖自守形式、L-函数、谱理论及表示理论等方面的内容，既给出了自守形式与L-函数很好的介绍，也指出了其算术应用。《自守形式与L-函数》不仅是本领域专家们有价值的参考书，也是研究生开展研究时极好的入门书。