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| 內容簡介： |
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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。刘建亚主编的《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。
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| 目錄：
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L-functions and Functoriality
James W. Cogdell
Ⅰ L-functions for GLn and Converse Theorems
1 Modular Forms and Automorphic Representations
2 L-functions for Gi 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
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