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Item Details
| Title:
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LECTURES ON AUTOMORPHIC $L$-FUNCTIONS
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| By: |
James W. Cogdell, Henry H. Kim, Maruti Ram Murty |
| Format: |
Paperback |
| List price:
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£69.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821848003 |
| ISBN 13: |
9780821848005 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 January, 2004 |
| Series: |
Fields Institute Monographs No. 20 |
| Pages: |
283 |
| Synopsis: |
This book provides a comprehensive account of the crucial role automorphic $L$-functions play in number theory and in the Langlands program, especially the Langlands functoriality conjecture. There has been a recent major development in the Langlands functoriality conjecture by the use of automorphic $L$-functions, namely, by combining converse theorems of Cogdell and Piatetski-Shapiro with the Langlands-Shahidi method. This book provides a step-by-step introduction to these developments and explains how the Langlands functoriality conjecture implies solutions to several outstanding conjectures in number theory, such as the Ramanujan conjecture, Sato-Tate conjecture, and Artin's conjecture. It would be ideal for an introductory course in the Langlands program. Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Table of Contents: James W.Cogdell, Lectures on $L$-functions, converse theorems, and functoriality for $GL_n$ : Preface; Modular forms and their $L$-functions; Automorphic forms; Automorphic representations; Fourier expansions and multiplicity one theorems; Eulerian integral representations; Local $L$-functions: The non-Archimedean case; The unramified calculation; Local $L$-functions: The Archimedean case; Global $L$-functions; Converse theorems; Functoriality; Functoriality for the classical groups; Functoriality for the classical groups, II. Henry H.Kim, Automorphic $L$-functions: Introduction; Chevalley groups and their properties; Cuspidal representations; $L$-groups and automorphic $L$-functions; Induced representations; Eisenstein series and constant terms; $L$-functions in the constant terms; Meromorphic continuation of $L$-functions; Generic representations and their Whittaker models; Local coefficients and non-constant terms; Local Langlands correspondence; Local $L$-functions and functional equations; Normalization of intertwining operators; Holomorphy and bounded in vertical strips; Langlands functoriality conjecture; Converse theorem of Cogdell and Piatetski-Shapiro; Functoriality of the symmetric cube; Functoriality of the symmetric fourth; Bibliography. M.Ram Murty, Applications of symmetric power $L$-functions: Preface; The Sato-Tate conjecture; Maass wave forms; The Rankin-Selberg method; Oscillations of Fourier coefficients of cusp forms; Poincare series; Kloosterman sums and Selberg's conjecture; Refined estimates for Fourier coefficients of cusp forms; Twisting and averaging of $L$-series; The Kim-Sarnak theorem; Introduction to Artin $L$-functions; Zeros and poles of Artin $L$-functions; The Langlands-Tunnell theorem; Bibliography. This is a reprint of the 2004 original. (FIM/20.S) |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Non-returnable |
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