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An Introduction to the Langlands Program

  • Textbook
  • © 2004

Overview

Authors:
  1. D. Bump
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  2. J. W. Cogdell
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  3. E. Shalit
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  4. D. Gaitsgory
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  5. E. Kowalski
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  6. S. S. Kudla
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Editors:
  1. Joseph Bernstein

    1. Department of Mathematics, Tel Aviv University, Tel Aviv, Israel

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  2. Stephen Gelbart

    1. Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel

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  • Self-contained presentation
  • A variety of areas in number theory from the classical zeta function up to the Langlands program are covered
  • Exposition is systematic, with each chapter focusing on a particular topic devoted to special cases of the program

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About this book

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.

Covered are a variety of areas in number theory from the classical zeta function up to the Langlands program. The exposition is sytematic, with each chapter focusing on a particular topic devoted to special cases of the program, and accessible to graduate students and researchers in the field.

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Elementary Theory of L-Functions I

    • E. Kowalski
    Pages 1-20

  3. Elementary Theory of L-Functions II

    • E. Kowalski
    Pages 21-37

  4. Classical Automorphic Forms

    • E. Kowalski
    Pages 39-71

  5. Artin L Functions

    • Ehud de Shalit
    Pages 73-87

  6. L-Functions of Elliptic Curves and Modular Forms

    • Ehud de Shalit
    Pages 89-108

  7. Tate’s Thesis

    • Stephen S. Kudla
    Pages 109-131

  8. From Modular Forms to Automorphic Representations

    • Stephen S. Kudla
    Pages 133-151

  9. Spectral Theory and the Trace Formula

    • Daniel Bump
    Pages 153-196

  10. Analytic Theory of L-Functions for GL n

    • J. W. Cogdell
    Pages 197-228

  11. Langlands Conjectures for GL n

    • J. W. Cogdell
    Pages 229-249

  12. Dual Groups and Langlands Functoriality

    • J. W. Cogdell
    Pages 251-268

  13. Informal Introduction to Geometric Langlands

    • D. Gaitsgory
    Pages 269-281
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Reviews

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)

Editors and Affiliations

  • Department of Mathematics, Tel Aviv University, Tel Aviv, Israel

    Joseph Bernstein

  • Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    Stephen Gelbart

Bibliographic Information

  • Book Title: An Introduction to the Langlands Program

  • Authors: D. Bump, J. W. Cogdell, E. Shalit, D. Gaitsgory, E. Kowalski, S. S. Kudla

  • Editors: Joseph Bernstein, Stephen Gelbart

  • DOI: https://doi.org/10.1007/978-0-8176-8226-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2004

  • Softcover ISBN: 978-0-8176-3211-3Published: 20 May 2003

  • eBook ISBN: 978-0-8176-8226-2Published: 11 December 2013

  • Edition Number: 1

  • Number of Pages: IX, 281

  • Topics: Number Theory, Algebraic Geometry, Topological Groups, Lie Groups

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