An Introduction to the Langlands Program [Paperback]

This book presents 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. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.

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 ShimuraTaniyamaWeil (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, whicl³D