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An Introduction to the Langlands Program paper IX, 281 p. 03

Bernstein, Joseph, Gelbart, Stephen  編
在庫状況 海外在庫有り  お届け予定日 1ヶ月  数量 冊 
価格 \21,352(税込)         

発行年月 2003年05月
出版社/提供元
出版国 スイス
言語 英語
媒体 冊子
装丁 paper
ページ数/巻数 IX, 281 p.
ジャンル 洋書/理工学/数学/代数学
ISBN 9780817632113
商品コード 0200317834
本の性格 テキスト
新刊案内掲載月 2003年06月
書評掲載誌 Choice
商品URL
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https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=0200317834

内容

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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