Spectral decomposition and Eisenstein series : une paraphrase de l'écriture / C. Moeglin, J.-L. Waldspurger.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

I. Hypotheses, automorphic forms, constant terms. I.1. Hypotheses and general notation. I.2. Automorphic forms: growth, constant terms. I.3. Cuspidal components. I.4. Upper bounds as functions of the constant term -- II. Decomposition according to cuspidal data. II. 1. Definitions. II. 2. Calculation of the scalar product of two pseudo-Eisenstein series -- III. Hilbertian operators and automorphic forms. III. 1. Hilbertian operators. III. 2. A decomposition of the space of automorphic forms. III. 3. Cuspidal exponents and square integrable automorphic forms -- IV. Continuation of Eisenstein series. IV. 1. The results. IV. 2. Some preparations. IV. 3. The case of relative rank 1. IV. 4. The general case -- V. Construction of the discrete spectrum via residues. V.1. Generalities and the residue theorem. V.2. Decomposition of the scalar product of two pseudo-Eisenstein series. V.3. Decomposition along the spectrum of the operators [Delta](f).

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 towards 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. It will be welcomed by number theorists, representation theorists and all whose work involves the Langlands program.