An Introduction to the Langlands Program

Medientyp: E-Book

Titel: An Introduction to the Langlands Program

Beteiligte: Bump, D. [Verfasser:in]; Cogdell, J. W. [Sonstige Person, Familie und Körperschaft]; Shalit, E. [Sonstige Person, Familie und Körperschaft]; Gaitsgory, Dennis [Sonstige Person, Familie und Körperschaft]; Kowalski, E. [Sonstige Person, Familie und Körperschaft]; Kudla, Stephen S. [Sonstige Person, Familie und Körperschaft]; Bernstein, Joseph [Herausgeber:in]; Gelbart, Stephen S. [Herausgeber:in]

Erschienen: Boston, MA: Birkhäuser, 2004

Umfang: Online-Ressource (IX, 281 p, online resource)

Sprache: Englisch

DOI: 10.1007/978-0-8176-8226-2

ISBN: 9780817682262

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Schlagwörter: Geometry, algebraic ; Mathematics ; Topological Groups ; Number theory ; Algebraic geometry. ; Lie groups.

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Beschreibung: 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 beautiful text

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