About this book
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.
- Book Title Arthur's Invariant Trace Formula and Comparison of Inner Forms
- DOI https://doi.org/10.1007/978-3-319-31593-5
- Copyright Information Springer International Publishing Switzerland 2016
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-319-31591-1
- Softcover ISBN 978-3-319-81073-7
- eBook ISBN 978-3-319-31593-5
- Edition Number 1
- Number of Pages XI, 567
- Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
Group Theory and Generalizations
Linear and Multilinear Algebras, Matrix Theory
Topological Groups, Lie Groups
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