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Spectral Decomposition and Eisenstein Series: A Paraphrase of the Scriptures (Cambridge Tracts in Mathematics, Series Number 113,Used
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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 ArthurSelberg trace formula. To make the book reasonably selfcontained, the authors also provide essential background in subjects such as: automorphic forms; Eisenstein series; Eisenstein pseudoseries, 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.
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