from International Press

Advanced Lectures in Mathematics, Vol. 9

Automorphic Forms and the Langlands Program

Edited by
Lizhen Ji (University of Michigan)
Kefeng Liu (University of California at Los Angeles)
Shing-Tung Yau (Harvard University)
Zhu-Jun Zheng (Henan University)

Publication Details

Softcover. 319 pages.
ISBN: 978-1-57146-141-4
Published: March 2010
Publisher: International Press of Boston
List price: $55.00. Discounts may apply.

Full Description

Classical modular forms on the upper half plane, with respect to the modular group SL(2,Z) and its congruence subgroups, have arisen naturally in number theory, complex analysis, topology, mathematical physics, and many other subjects. The closely related automorphic representations are basic notions in the celebrated Langlands program, which was proposed by Langlands in the late 1960s and has since revolutionized the fields of number theory, arithmetic algebraic geometry, and representation theory. This volume consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program.

Table of Contents

• Prerequisites for the Langlands Program
  A. W. Knapp
• First Steps with the Langlands Program
  A. W. Knapp
• Class Field Theory, the Langlands Program and its Application to Number Theory
  Stephen S. Gelbart
• Automorphic Forms and Automorphic Representations
  Wee Teck Gan
• Introductory Notes on the Trace Formula
  Erez M. Lapid
• Euler Products and Twisted Euler Products
  Solomon Friedberg
• Arithmetic Trace Formulas and Kloostermania
  Xiaoqing Li
• Tempered Endoscopy for Real Groups II: Spectral Transfer Factors
  D. Shelstad
• Algebraic Birkhoff Decomposition and Its Applications
  Li Guo

About the Series

Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cutting-edge results.

Other volumes in the Advanced Lectures in Mathematics series

Vol. 12. Cohomology of Groups and Algebraic K-theory

Vol. 11. Recent Advances in Geometric Analysis

Vol. 10. Trends in Partial Differential Equations

Vol. 8. Recent Developments in Algebra and Related Areas

Vol. 7. Handbook of Geometric Analysis, No. 1

Vol. 6. Geometry, Analysis and Topology of Discrete Groups

Vol. 5. Fourth International Congress of Chinese Mathematicians (2007)

Vol. 4. Variational Principles for Discrete Surfaces

Vol. 3. Computational Conformal Geometry

Vol. 2. Asymptotic Theory in Probability and Statistics with Applications

Vol. 1. Superstring Theory

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