An Introduction to the Langlands Program
Editors: Bernstein, Joseph, Gelbart, Steve (Eds.)
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- About this Textbook
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For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.
The twelve chapters of this monograph present a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics.
Key features of this self-contained presentation:
A variety of areas in number theory from the classical zeta function up to the Langlands program are covered.
The exposition is systematic, with each chapter focusing on a particular topic devoted to special cases of the program:
• Basic zeta function of Riemann and its generalizations to Dirichlet and Hecke L-functions, class field theory and some topics on classical automorphic functions (E. Kowalski)
• A study of the conjectures of Artin and Shimura–Taniyama–Weil (E. de Shalit)
• An examination of classical modular (automorphic) L-functions as GL(2) functions, bringing into play the theory of representations (S.S. Kudla)
• Selberg's theory of the trace formula, which is a way to study automorphic representations (D. Bump)
• Discussion of cuspidal automorphic representations of GL(2,(A)) leads to Langlands theory for GL(n) and the importance of the Langlands dual group (J.W. Cogdell)
• An introduction to the geometric Langlands program, a new and active area of research that permits using powerful methods of algebraic geometry to construct automorphic sheaves (D. Gaitsgory)
Graduate students and researchers will benefit from this beautiful text.
- Reviews
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From the reviews:
"The six chapters of this monograph give a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. First-year graduate students and researchers will benefit from this beautiful text."
--Zentralblatt Math
". . . the present volume constitutes the most readable entree into the subject to date, suitable both for serious reading and for browsing, and should attract a new generation to this exciting subject. . . . Recommended."
--CHOICE
“I suspect this book will find its way into the hands of many graduate students. Perhaps it will also motivate a few of them to learn more, get involved, and make their own contributions.” (MAA REVIEWS)
- Table of contents (12 chapters)
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Elementary Theory of L-Functions I
Pages 1-20
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Elementary Theory of L-Functions II
Pages 21-37
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Classical Automorphic Forms
Pages 39-71
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Artin L Functions
Pages 73-87
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L-Functions of Elliptic Curves and Modular Forms
Pages 89-108
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- An Introduction to the Langlands Program
- Editors
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- Joseph Bernstein
- Steve Gelbart
- Copyright
- 2004
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Birkhäuser Boston
- eBook ISBN
- 978-0-8176-8226-2
- DOI
- 10.1007/978-0-8176-8226-2
- Softcover ISBN
- 978-0-8176-3211-3
- Edition Number
- 1
- Number of Pages
- IX, 281
- Topics
