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Arthur's Invariant Trace Formula and Comparison of Inner Forms (Paperback, Softcover reprint of the original 1st ed. 2016)
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Arthur's Invariant Trace Formula and Comparison of Inner Forms (Paperback, Softcover reprint of the original 1st ed. 2016)
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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.
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