An Introduction to the Langlands Program:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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 |
| Beschreibung: | 1 Online-Ressource (IX, 281 p) |
| ISBN: | 9780817682262 9780817632113 |
| DOI: | 10.1007/978-0-8176-8226-2 |
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Datensatz im Suchindex
| _version_ | 1804153089609957376 |
|---|---|
| any_adam_object | |
| author | Bump, D. |
| author_facet | Bump, D. |
| author_role | aut |
| author_sort | Bump, D. |
| author_variant | d b db |
| building | Verbundindex |
| bvnumber | BV042419218 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)867181481 (DE-599)BVBBV042419218 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-8226-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817682262 9780817632113 |
| language | English |
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| spelling | Bump, D. Verfasser aut An Introduction to the Langlands Program by D. Bump, J. W. Cogdell, E. Shalit, D. Gaitsgory, E. Kowalski, S. S. Kudla ; edited by Joseph Bernstein, Stephen Gelbart Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (IX, 281 p) txt rdacontent c rdamedia cr rdacarrier 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 Mathematics Geometry, algebraic Topological Groups Number theory Number Theory Algebraic Geometry Topological Groups, Lie Groups Mathematik L-Funktion (DE-588)4137026-0 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s L-Funktion (DE-588)4137026-0 s 1\p DE-604 Cogdell, J. W. Sonstige oth Shalit, E. Sonstige oth Gaitsgory, D. Sonstige oth Kowalski, E. Sonstige oth Kudla, S. S. Sonstige oth Bernstein, Joseph Sonstige oth Gelbart, Stephen Sonstige oth https://doi.org/10.1007/978-0-8176-8226-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bump, D. An Introduction to the Langlands Program Mathematics Geometry, algebraic Topological Groups Number theory Number Theory Algebraic Geometry Topological Groups, Lie Groups Mathematik L-Funktion (DE-588)4137026-0 gnd Automorphe Form (DE-588)4003972-9 gnd |
| subject_GND | (DE-588)4137026-0 (DE-588)4003972-9 |
| title | An Introduction to the Langlands Program |
| title_auth | An Introduction to the Langlands Program |
| title_exact_search | An Introduction to the Langlands Program |
| title_full | An Introduction to the Langlands Program by D. Bump, J. W. Cogdell, E. Shalit, D. Gaitsgory, E. Kowalski, S. S. Kudla ; edited by Joseph Bernstein, Stephen Gelbart |
| title_fullStr | An Introduction to the Langlands Program by D. Bump, J. W. Cogdell, E. Shalit, D. Gaitsgory, E. Kowalski, S. S. Kudla ; edited by Joseph Bernstein, Stephen Gelbart |
| title_full_unstemmed | An Introduction to the Langlands Program by D. Bump, J. W. Cogdell, E. Shalit, D. Gaitsgory, E. Kowalski, S. S. Kudla ; edited by Joseph Bernstein, Stephen Gelbart |
| title_short | An Introduction to the Langlands Program |
| title_sort | an introduction to the langlands program |
| topic | Mathematics Geometry, algebraic Topological Groups Number theory Number Theory Algebraic Geometry Topological Groups, Lie Groups Mathematik L-Funktion (DE-588)4137026-0 gnd Automorphe Form (DE-588)4003972-9 gnd |
| topic_facet | Mathematics Geometry, algebraic Topological Groups Number theory Number Theory Algebraic Geometry Topological Groups, Lie Groups Mathematik L-Funktion Automorphe Form |
| url | https://doi.org/10.1007/978-0-8176-8226-2 |
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