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Decomposition Spectrale et Series d'Eisenstein (French, Hardcover, 1993 ed.)
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Decomposition Spectrale et Series d'Eisenstein (French, Hardcover, 1993 ed.)
Series: Progress in Mathematics, 113
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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.
The present 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 have also
provided essential background to subjects such as automorphic
forms, Eisenstein series, Eisenstein pseudo-series (or
wave-packets) and their properties. It is thus also an
introduction, suitable for graduate students, to the theory of
automorphic forms, written using contemporary terminology. It will
be welcomed by number theorists, representation theorists, and all
whose work involves the Langlands program.
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