An Introduction to Automorphic Representations
Language: English
Published by Springer, Springer Mär 2024, 2024
- Hardcover
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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
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This item is printed on demand - it takes 3-4 days longer - Neuware -The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics.The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields.The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed.This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface. 628 pp. Englisch.…
Seller Inventory # 9783031411519
- Title
- An Introduction to Automorphic Representations
- Author
- Jayce R. Getz
- Publisher
- Springer, Springer Mär 2024
- Publication year
- 2024
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 303141151X
- ISBN 13
- 9783031411519
- Item weight
- 1,212 grams
- Dimensions
- 241x160x37 mm
The goal of this textbook is to introduce and study automorphic representations, objects at the very core of the Langlands Program. It is designed for use as a primary text for either a semester or a year-long course, for the independent study of advanced topics, or as a reference for researchers. The reader is taken from the beginnings of the subject to the forefront of contemporary research. The journey provides an accessible gateway to one of the most fundamental areas of modern mathematics, with deep connections to arithmetic geometry, representation theory, harmonic analysis, and mathematical physics.
The first part of the text is dedicated to developing the notion of automorphic representations. Next, it states a rough version of the Langlands functoriality conjecture, motivated by the description of unramified admissible representations of reductive groups over nonarchimedean local fields. The next chapters develop the theory necessary to make the Langlands functoriality conjecture precise. Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings. This preparation complete, the global Langlands functoriality conjectures are stated and known cases are discussed.
This is followed by a treatment of distinguished representations in global and local settings. The link between distinguished representations and geometry is explained in a chapter on the cohomology of locally symmetric spaces (in particular, Shimura varieties). The trace formula, an immensely powerful tool in the Langlands Program, is discussed in the final chapters of the book. Simple versions of the general relative trace formulae are treated for the first time in a textbook, and a wealth of related material on algebraic group actions is included. Outlines for several possible courses are provided in the Preface.
"Synopsis" may belong to another edition of this title.
About the Author
Jayce R. Getz is Associate Professor of Mathematics at Duke University. His research in number theory spans several subjects --- algebraic geometry, automorphic representations, harmonic analysis, and trace formulae. His monograph with M. Goresky (Institute for Advanced Studies), Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change, was awarded the 2011 Ferran Sunyer i Balaguer Prize.
Heekyoung Hahn is Associate Research Professor of Mathematics at Duke University. Her research covers additive combinatorics, Langlands functoriality, and related issues in the representation theory of algebraic groups."About the title" may belong to another edition of this title.
BuchWeltWeit Ludwig Meier e.K.
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