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Spectral Theory of the Riemann Zeta-Function

$82.99 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: January 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521058070

$ 82.99 (C)
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  • This ground-breaking work combines the classic (the zeta-function) with the modern (the spectral theory) to create a comprehensive but elementary treatment of spectral resolution. The story starts with a basic but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. The author achieves this by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory. These ideas are then utilized to unveil a new image of the zeta-function, revealing it as 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 recent development of number theory. Mathematics specialists and researchers will find this a fascinating work.

    • New view of zeta functions
    • One of most important topics in number theory
    • Contains the first elementary but unabridged treatment of this approach
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    Reviews & endorsements

    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, International Mathematical News

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    Product details

    • Date Published: January 2008
    • format: Paperback
    • isbn: 9780521058070
    • length: 240 pages
    • dimensions: 230 x 152 x 15 mm
    • weight: 0.396kg
    • availability: Available
  • Table of Contents

    1. Non-Euclidean harmonics
    2. Trace formulas
    3. Automorphic L-functions
    4. An explicit formula
    5. Asymptotics
    References
    Index.

  • Author

    Yoichi Motohashi, Nihon University, Tokyo

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