Lectures on automorphic L-functions / James W. Cogdell, Henry H. Kim, M. Ram Murty.

Format:

Book

Author/Creator:

Cogdell, James W., 1953- author.

Contributor:

Kim, Henry Hyeongsin, 1964-

Murty, Maruti Ram.

Series:

Fields Institute Monographs, 2472-4173 ; v. 20

Language:

English

Subjects (All):

L-functions.

Automorphic functions.

Physical Description:

1 online resource (xii, 283 pages)

Place of Publication:

Providence, R.I. : American Mathematical Society, c2004.

System Details:

Mode of access : World Wide Web

Contents:

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 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 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 Selberg's 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

Notes:

Includes bibliographical references (pages 281-283).

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record.

Other Format:

Print version: Cogdell, James W., 1953- Lectures on automorphic L-functions /

ISBN:

9781470431471 (online)

Access Restriction:

Restricted for use by site license.