By C. Moeglin
By J.-L. Waldspurger
Cambridge Tracts in Mathematics
Publisher: Cambridge University Press
Print Publication Year:1995
Online Publication Date:September 2009
The decomposition of the space L2 (G(Q)\G(A)), where G is a reductive group defined over Q and A is the ring of adeles of Q, is a deep problem at the intersection of number and group theory. Langlands reduced this decomposition to that of the (smaller) spaces of cuspidal automorphic forms for certain subgroups of G. This book describes this proof in detail. The starting point is the theory of automorphic forms, which can also serve as a first step toward understanding the Arthur-Selberg trace formula. To make the book reasonably self-contained, the authors also provide essential background in subjects such as: automorphic forms; Eisenstein series; Eisenstein pseudo-series, and their properties. It is thus also an introduction, suitable for graduate students, to the theory of automorphic forms, the first written using contemporary terminology.
I - Hypotheses, automorphic forms, constant terms
II - Decomposition according to cuspidal data
III - Hilbertian operators and automorphic forms
IV - Continuation of Eisenstein series
V - Construction of the discrete spectrum via residues
No references available.