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An Introduction to the Langlands Program
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An Introduction to the Langlands Program

An Introduction to the Langlands Program

Daniel Bump, J.W. Cogdell, D. Gaitsgory, E. De Shalit, Emmanuel Kowalski, S.S. Kudla

282 pages, parution le 15/01/2003

Résumé

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.

Written for: Researchers, graduate students

L'auteur - Daniel Bump

Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include Automorphic Forms and Representations (Cambridge University Press 1997) and Algebraic Geometry (World Scientific 1998).

L'auteur - Emmanuel Kowalski

Emmanuel Kowalski est professeur à l'Université Bordeaux I. Ses travaux portent sur la théorie analytique des nombres, en particulier les aspects analytiques des fonctions L et des formes automorphes, et leurs interactions avec la géométrie arithmétique.

Sommaire

  • E. Kowalski - Elementary Theory of L-Functions I
  • E. Kowalski - Elementary Theory of L-Functions II
  • E. Kowalski - Classical Automorphic Forms
  • E. DeShalit - Artin L-Functions
  • E. DeShalit - L-Functions of Elliptic Curves and Modular Forms
  • S. Kudla - Tate's Thesis
  • S. Kudla - From Modular Forms to Automorphic Representations
  • D. Bump - Spectral Theory and the Trace Formula
  • J. Cogdell - Analytic Theory of L-Functions for GLn
  • J. Cogdell - Langlands Conjectures for GLn
  • J. Cogdell - Dual Groups and Langlands Functoriality
  • D. Gaitsgory - Informal Introduction to Geometric Langlands
Voir tout
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Daniel Bump, J.W. Cogdell, D. Gaitsgory, E. De Shalit, Emmanuel Kowalski, S.S. Kudla
Parution 15/01/2003
Nb. de pages 282
Format 15,5 x 23,5
Couverture Broché
Poids 420g
Intérieur Noir et Blanc
EAN13 9780817632113
ISBN13 978-0-8176-3211-3

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