Arthur's Invariant Trace Formula and Comparison of Inner Forms

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.