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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: J. Bernstein and with contributions by D. Bump S. Gelbart (Editors), J. W. Cogdell
Title: Introduction to the Langlands program
Additional book information: Birkhäuser, Boston, 2003, x + 281 pp., ISBN 0-8176-3211-5, $39.95$

References [Enhancements On Off] (What's this?)

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C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of elliptic curves over $\mathbb{Q} $, J. Am. Math. Soc., 14 (2001) 843-939. MR 1839918
[CKPSS]
J. W. Cogdell, H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to $GL_{n}$, Publ. Math. IHES, 93 (2001) 5-30; II (manuscript, 2003). MR 1863734
[GRS]
D. Ginzburg, S. Rallis, and D. Soudry, Generic automorphic forms on $SO_{2n+1}$: functorial lift to $GL_{2n}$, endoscopy, and base change. Internat. Math. Res. Notices, 14 (2001), 729-764. MR 1846354
[HT]
M. Harris and R. Taylor, On the geometry and cohomology of some simple Shimura varieties, Annals of Math. Studies, 151 (2001). MR 1876802
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G. Henniart, Une preuve simple des conjectures de Langlands pour $GL(n)$ sur un corps $p$-adique, Invent. Math., 139 (2000) 439-455. MR 1738446
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L. Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002) 1-241. MR 1875184
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G. Laumon, M. Rapoport, and U. Stuhler, $\mathcal{D}$-elliptic sheaves and the Langlands correspondence, Invent. Math., 113 (1993) 217-338. MR 1228127
[S]
F. Shahidi, Automorphic $L$-functions and functoriality, Proceedings of the ICM 2002, Vol. II (2002) 655-666. MR 1957073
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R. Taylor and A. Wiles, Ring theoretic properties of certain Hecke algebras, Annals of Math., 141 (1995) 553-572. MR 1333036
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A. Wiles, Modular elliptic curves and Fermat's last theorem, Annals of Math., 141 (1995) 443-551. MR 1333035
Review Information:

Reviewer: Michael Harris
Affiliation: Université Paris 7
Email: harris@math.jussieu.fr
Journal: Bull. Amer. Math. Soc. 41 (2004), 257-266
Published electronically: January 20, 2004
Review copyright: © Copyright 2004 American Mathematical Society