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|a 10.1007/978-0-8176-8226-2
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|a An Introduction to the Langlands Program
|h [electronic resource] /
|c edited by Joseph Bernstein, Stephen Gelbart.
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| 250 |
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|a 1st ed. 2004.
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| 264 |
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|a Boston, MA :
|b Birkhäuser Boston :
|b Imprint: Birkhäuser,
|c 2004.
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| 300 |
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|a IX, 281 p.
|b online resource.
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|a text
|b txt
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|a Springer eBook Collection
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|a 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.
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| 520 |
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|a 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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|a Loaded electronically.
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| 590 |
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|a Electronic access restricted to members of the Holy Cross Community.
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|a Number theory.
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| 650 |
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|a Algebraic geometry.
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| 650 |
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|a Topological groups.
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| 650 |
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|a Lie groups.
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| 690 |
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|a Electronic resources (E-books)
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| 700 |
1 |
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|a Bernstein, Joseph.
|e editor.
|4 edt
|4 http://id.loc.gov/vocabulary/relators/edt
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| 700 |
1 |
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|a Gelbart, Stephen.
|e editor.
|4 edt
|4 http://id.loc.gov/vocabulary/relators/edt
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| 710 |
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|a SpringerLink (Online service)
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| 830 |
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|a Springer eBook Collection.
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://doi.org/10.1007/978-0-8176-8226-2
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