An Introduction to the Langlands Program

Joseph Bernstein, Bernstein, Joseph, Joseph Bernstein, Stephen Gelbart, S.S. Kudla, E. Kowalski, E. de Shalit, D. Gaitsgory, J.W. Cogdell, D. Bump

ISBN 10: 0817632115 / ISBN 13: 9780817632113

Published by Birkhauser Boston Inc, US, 2003

About this Item

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.

Seller Inventory # LU-9780817632113

Bibliographic Details

• Title: An Introduction to the Langlands Program
• Publisher: Birkhauser Boston Inc, US
• Publication Date: 2003
• Language: English
• ISBN 10: 0817632115
• ISBN 13: 9780817632113
• Binding: Paperback
• Edition: 2004 ed.
• Condition: New
• Dimensions: 15.49W x 1.68H x 23.5D centimeters 15.49 centimeters width by 1.68 centimeters height by 23.5 centimeters depth

About this title

Synopsis

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.

From the Back Cover

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 beautifultext.