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  3. Spectral Theory of the Riemann Zeta-Function
  • Cited by 94
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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2011
      September 1997
      ISBN:
      9780511983399
      9780521445207
      9780521058070
      DOI:
      https://doi.org/10.1017/CBO9780511983399
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.455kg, 240 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.396kg, 240 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory
      Series:
      Cambridge Tracts in Mathematics (127)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory
    Series:
    Cambridge Tracts in Mathematics (127)
    Information

    Book description

    The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.

    Reviews

    Review of the hardback:‘… gives an excellent presentation of the interplay between the Riemann zeta function and automorphic forms … nicely written and of great interest for any number theorists.’

    R. Tichy Source: International Mathematical News

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