Arthur's Invariant Trace Formula and Comparison of Inner Forms
Authors: Flicker, Yuval
Free Preview- A synthesis of two decades worth of research, combining results from Arthur’s many articles into one cohesive and accessible text
- Author introduces the material in stages, balancing the need to motivate the reader while exploring the larger, more technical details
- Will be a valuable resource as both a reference for researchers and as a tool for advanced graduate students in this area
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- About this book
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This monograph provides an accessible and comprehensive introduction to James Arthur’s invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur’s research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details.
The book begins with a brief overview of Arthur’s work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur’s proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G’ = GL(n) and its inner form G< and for functions with matching orbital integrals.
Arthur’s Invariant Trace Formula and Comparison of Inner Forms will appeal to advanced graduate students, researchers, and others interested in automorphic forms and trace formulae. Additionally, it can be used as a supplemental text in graduate courses on representation theory. - Reviews
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“In the book under review, the main original articles, together with a plethora of related details, that required to understand the trace formula theory, have been unified and written in a uniform, compact and self-contained way. … this book presents an excellent source for readers interested in the trace formula and its applications and should definitely make the process of entering the considered subject a lot easier both for graduate students and for interested researchers.” (Ivan Matić, zbMATH 1359.22014, 2017)
- Table of contents (6 chapters)
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Introduction
Pages 1-23
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Local Theory
Pages 25-137
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Arthur’s Noninvariant Trace Formula
Pages 139-214
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Study of Noninvariance
Pages 215-316
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The Invariant Trace Formula
Pages 317-439
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Table of contents (6 chapters)
- Download Preface 1 PDF (47.7 KB)
- Download Sample pages 1 PDF (1.1 MB)
- Download Table of contents PDF (41.1 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Arthur's Invariant Trace Formula and Comparison of Inner Forms
- Authors
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- Yuval Flicker
- Copyright
- 2016
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-31593-5
- DOI
- 10.1007/978-3-319-31593-5
- Hardcover ISBN
- 978-3-319-31591-1
- Softcover ISBN
- 978-3-319-81073-7
- Edition Number
- 1
- Number of Pages
- XI, 567
- Number of Illustrations
- 3 b/w illustrations
- Topics
