An Introduction to the Langlands Program (Paperback)

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• Format: Paperback   Learn more about the Paperback format using Tower WIKI.
• Publisher: Springer Verlag
• ISBN: 0817632115
• WAPI (Tower ID): 100955528
• Release Date: June 1, 2003
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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:

a 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 A study of the conjectures of Artin and Shimuraa "Taniyamaa "Weil (E. de Shalit)

a An examination of classical modular (automorphic) L-functions as GL(2) functions, bringing into play the theory of representations (S.S. Kudla)

a Selberg's theory of the trace formula, which is a way to study automorphic representations (D. Bump)

a 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)

a 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 benefitfrom this beautiful text.

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