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＜電子ブック＞
An Introduction to the Langlands Program / edited by Joseph Bernstein, Stephen Gelbart

版	1st ed. 2004.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2004
本文言語	英語
大きさ	IX, 281 p : online resource
著者標目	Bernstein, Joseph editor Gelbart, Stephen editor SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Algebraic geometry LCSH:Topological groups LCSH:Lie groups FREE:Number Theory FREE:Algebraic Geometry FREE:Topological Groups and Lie Groups
一般注記	Preface -- E. Kowalski - Elementary Theory of L-Functions I -- E. Kowalski - Elementary Theory of L-Functions II -- E. Kowalski - Classical Automorphic Forms -- E. DeShalit - Artin L-Functions -- E. DeShalit - L-Functions of Elliptic Curves and Modular Forms -- S. Kudla - Tate's Thesis -- S. Kudla - From Modular Forms to Automorphic Representations -- D. Bump - Spectral Theory and the Trace Formula -- J. Cogdell - Analytic Theory of L-Functions for GLn -- J. Cogdell - Langlands Conjectures for GLn -- J. Cogdell - Dual Groups and Langlands Functoriality -- D. Gaitsgory - Informal Introduction to Geometric Langlands 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 beautifultext HTTP:URL=https://doi.org/10.1007/978-0-8176-8226-2

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