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  3. Automorphic Forms on SL2 (R)
  • Cited by 24
      • Armand Borel, Institute for Advanced Study, Princeton, New Jersey
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    • Publisher:
      Cambridge University Press
      Publication date:
      October 2011
      August 1997
      ISBN:
      9780511896064
      9780521580496
      9780521072120
      DOI:
      https://doi.org/10.1017/CBO9780511896064
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.44kg, 208 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.31kg, 208 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
      Series:
      Cambridge Tracts in Mathematics (130)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Discrete Mathematics Information Theory and Coding
    Series:
    Cambridge Tracts in Mathematics (130)
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    Book description

    This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\"G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\"G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book.

    Reviews

    Review of the hardback:‘This text will serve as an admirable introduction to harmonic analysis as it appears in contemporary number theory and algebraic geometry.’

    Victor Snaith Source: Bulletin of the London Mathematical Society

    Review of the hardback:‘… carefully and concisely written … Clearly every mathematical library should have this book.’

    Source: Zentralblatt

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