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  3. Spectral Decomposition and Eisenstein Series
  • Cited by 194
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      November 1995
      ISBN:
      9780511470905
      9780521418935
      9780521070355
      DOI:
      https://doi.org/10.1017/CBO9780511470905
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.656kg, 368 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.54kg, 368 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Algebra
      Series:
      Cambridge Tracts in Mathematics (113)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Algebra
    Series:
    Cambridge Tracts in Mathematics (113)
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    Book description

    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.

    Reviews

    Review of the hardback:‘… a superb introduction to analytic theory of automorphic forms.’

    Source: European Mathematical Society Newsletter

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