Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120) (Annals of Mathematics Studies) - James Arthur, Laurent Clozel (1989)
ISBN 0691085188
Subject Automorphic forms; Representations of groups; Trace formulas
Publisher Princeton University Press
Publication Date 6/1/1989
Format Paperback (229 x 152 mm)
Language e

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences.

This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.

Personal Details
Collection Status In Collection
Index 474
Read It Yes
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Product Details
LoC Classification QA171 .A78 1989
Dewey 512/.2
Cover Price $45.00
No. of Pages 248