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Spectral Decomposition and Eisenstein Series
A Paraphrase of the Scriptures


Part of Cambridge Tracts in Mathematics

  • Date Published: July 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521070355

£ 66.99

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About the Authors
  • 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.

    • First book on subject using modern terminology
    • First aimed at graduate students
    • Leading authors
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    Reviews & endorsements

    Review of the hardback: '… a superb introduction to analytic theory of automorphic forms.' European Mathematical Society Newsletter

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    Product details

    • Date Published: July 2008
    • format: Paperback
    • isbn: 9780521070355
    • length: 368 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.54kg
    • contains: 6 b/w illus. 4 tables
    • availability: Available
  • Table of Contents

    1. Hypotheses, automorphic forms, constant terms
    2. Decomposition according to cuspidal data
    3. Hilbertian operators and automorphic forms
    4. Continuation of Eisenstein series
    5. Construction of the discrete spectrum via residues
    6. Spectral decomposition via the discrete Levi spectrum
    Appendix I. Lifting of unipotent subgroups
    Appendix II. Automorphic forms and Eisenstein series on function fields
    Appendix III. On the discrete spectrum of G2
    Appendix IV. Non-connected groups

  • Authors

    C. Moeglin, Centre National de la Recherche Scientifique (CNRS), Paris

    J. L. Waldspurger, Centre National de la Recherche Scientifique (CNRS), Paris


    Leila Schneps

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