An introduction to the Langlands program. D. Bump, D. Gaitsgory, E. Kowalski, E. de Shalit, J.W. Cogdell, Joseph Bernstein, S.S. Kudla, Stephen Gelbart

An introduction to the Langlands program



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An introduction to the Langlands program D. Bump, D. Gaitsgory, E. Kowalski, E. de Shalit, J.W. Cogdell, Joseph Bernstein, S.S. Kudla, Stephen Gelbart ebook djvu
Publisher:
Language: English
Page: 293
ISBN: 0817632115, 9780817632113

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 six 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) 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.



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