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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.
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.
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.
A note to readers: This book is in French. The text has two
chapters. The first one, written by Waldspurger, proves a twisted
version of the local trace formula of Arthur over a local field.
This formula is an equality between two expressions, one involving
weighted orbital integrals, the other one involving weighted
characters. The authors follow Arthur's proof, but the treatement
of the spectral side is more complicated in the twisted situation.
They need to use the combinatorics of the ``Morning Seminar''. The
authors' local trace formula has the same consequences as in
Arthur's paper on elliptic characters. The second chapter, written
by Moeglin, gives a symmetric form of the local trace formula as in
Arthur's paper on Fourier Transform of Orbital integral and
describes any twisted orbital integral, in the p-adic case, as
integral of characters.
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