An Introduction to the Langlands Program (D. Bump, J. W. Cogdell, E. de Shalit etc.) (z-lib.org)

D. Bump
J. W. Cogdell
E. de Shalit
D. Gaitsgory
E. Kowalski
S.S. Kudla
An Introduction to the
Langlands Program
Joseph Bernstein
Stephen Gelbart
Editors
Springer Science+
Business Media, LLC

Joseph Bemstein
Stephen Gelbart
Tel Aviv University
Department of Mathematics
RamatAviv
The Weizmann Institute of Science
Department of Mathematics
Rehovot76100
Tel Aviv 69978
Israel
Israel
Ubrary of Congress Cataloging·in·Publlcation Data
An introduction to the Langlands program 1 Joseph Bernstein, Stephen Gelbart, editors ;
[with contributions
by] D. Bump ... [et al.).
p. cm.
Includes bibliographical references.
ISBN 0-8176-3211-5 (alk. paper)- ISBN 3-7643-3211-5 (alk. paper)
1. Automorphic forms. 2. L-functions. 1. Bernstein, Joseph, 1945- II. Gelbart, Stephen
s .. 1946-
QA353.A9159 2003
515'-dc21
ISBN 978-0-8176-3211-3 ISBN 978-0-8176-8226-2 (eBook)
DOI 10.1007/978-0-8176-8226-2
AMS Subject Classifications: IIMxx, 11Fxx, 14Hxx, 22Exx
Printed on acid-frec paper.
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© 2004 Springer Science+Business Media New York
Originally published by Birkhauser Boston in 2004
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Contents
Preface ............................................................ vii
1. Elementary Theory of L-Functions I
E. Kowalski ......................................................... 1
2. Elementary Theory of L-Functions II
E. Kowalski ....................................................... 21
3. Classical Automorphic Forms
E. Kowalski ....................................................... 39
4. Artin L Functions
Ehud de Shalit
..................................................... 73
5. L-Functions of Elliptic Curves and Modular Forms
Ehud de Shalit
..................................................... 89
6. Tate's Thesis
Stephen
S. Kudla .................................................. 109
7. From Modular Forms to Automorphic Representations
StephenS. Kudla
.................................................. 133
8. Spectral Theory and the Trace Formula
Daniel Bump
..................................................... 153
9. Analytic Theory of L-Functions for GLn
J. W. Cogdell ...................................................... 197
10. Langlands Conjectures for
GLn
J. W. Cogdell ...................................................... 229
11. Dual Groups and Langlands Functoriality
J. W. Cogdell ...................................................... 251
12. Informal Introduction to Geometric Langlands
D. Gaitsgory ..................................................... 269