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  3. Eisenstein Series and Automorphic Representations
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    • Publisher:
      Cambridge University Press
      Publication date:
      29 June 2018
      05 July 2018
      ISBN:
      9781316995860
      9781107189928
      DOI:
      https://doi.org/10.1017/9781316995860
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.92kg, 584 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Physics and Astronomy, Number Theory, Theoretical Physics and Mathematical Physics
      Series:
      Cambridge Studies in Advanced Mathematics (176)
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    Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Number Theory, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Studies in Advanced Mathematics (176)
    Information

    Book description

    This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.

    Reviews

    'This book provides a bridge between two very active and important parts of mathematics and physics, namely the theory of automorphic forms on reductive groups and string theory. The authors have masterfully presented both aspects and their connections, and have provided examples and details at all levels to make the book available to a large readership, including non-experts in both fields. This is a valuable contribution and a welcoming text for graduate students as well.’

    Freydoon Shahidi - Purdue University, Indiana

    'The book is a valuable addition to the literature, and it may inspire more exchange between mathematics and physics at an advanced level.'

    Anton Deitmar Source: MathSciNet

    ‘The prerequisites for a profitable reading this book are enormous. Readers without a solid background in algebraic and analytic number theory, classfield theory, modular forms and representation theory will only be able to read a couple of sections. Researchers in these fields will be grateful to the authors and the publisher for providing access to some rather advanced mathematics. The material is presented in a very clear and lucid way; there is an extensive index and a list of references containing 634 items.’

    Franz Lemmermeyer Source: zbMATH

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