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Lectures on Automorphic $L$-functions
About this Title
James W. Cogdell, Oklahoma State University, Stillwater, OK, Henry H. Kim, University of Toronto, Toronto, ON, Canada and M. Ram Murty, Queenâs University, Kingston, ON, Canada
Publication: Fields Institute Monographs
Publication Year:
2004; Volume 20
ISBNs: 978-0-8218-4800-5 (print); 978-1-4704-3147-1 (online)
DOI: https://doi.org/10.1090/fim/020
MathSciNet review: MR2071722
MSC: Primary 11F70; Secondary 22E55
Table of Contents
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Front/Back Matter
Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$, by James W. Cogdell
- Preface
- Lecture 1. Modular forms and their $L$-functions
- Lecture 2. Automorphic forms
- Lecture 3. Automorphic representations
- Lecture 4. Fourier expansions and multiplicity one theorems
- Lecture 5. Eulerian integral representations
- Lecture 6. Local $L$-functions: The non-Archimedean case
- Lecture 7. The unramified calculation
- Lecture 8. Local $L$-functions: The Archimedean case
- Lecture 9. Global $L$-functions
- Lecture 10. Converse theorems
- Lecture 11. Functoriality
- Lecture 12. Functoriality for the classical groups
- Lecture 13. Functoriality for the classical groups, II
Automorphic $L$-functions, by Henry H. Kim
- Introduction
- Chapter 1. Chevalley groups and their properties
- Chapter 2. Cuspidal representations
- Chapter 3. $L$-groups and automorphic $L$-functions
- Chapter 4. Induced representations
- Chapter 5. Eisenstein series and constant terms
- Chapter 6. $L$-functions in the constant terms
- Chapter 7. Meromorphic continuation of $L$-functions
- Chapter 8. Generic representations and their Whittaker models
- Chapter 9. Local coefficients and non-constant terms
- Chapter 10. Local Langlands correspondence
- Chapter 11. Local $L$-functions and functional equations
- Chapter 12. Normalization of intertwining operators
- Chapter 13. Holomorphy and bounded in vertical strips
- Chapter 14. Langlands functoriality conjecture
- Chapter 15. Converse theorem of Cogdell and Piatetski-Shapiro
- Chapter 16. Functoriality of the symmetric cube
- Chapter 17. Functoriality of the symmetric fourth
- Bibliography
Applications of symmetric power $L$-functions, by M. Ram Murty
- Preface
- Lecture 1. The Sato-Tate conjecture
- Lecture 2. Maass wave forms
- Lecture 3. The Rankin-Selberg method
- Lecture 4. Oscillations of Fourier coefficients of cusp forms
- Lecture 5. Poincaré series
- Lecture 6. Kloosterman sums and Selbergâs conjecture
- Lecture 7. Refined estimates for Fourier coefficients of cusp forms
- Lecture 8. Twisting and averaging of $L$-series
- Lecture 9. The Kim-Sarnak theorem
- Lecture 10. Introduction to Artin $L$-functions
- Lecture 11. Zeros and poles of Artin $L$-functions
- Lecture 12. The Langlands-Tunnell theorem
- Bibliography