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  3. The Theory of Hardy's Z-Function
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  • Publisher:
    Cambridge University Press
    Publication date:
    05 November 2012
    27 September 2012
    ISBN:
    9781139236973
    9781107028838
    DOI:
    https://doi.org/10.1017/CBO9781139236973
    Dimensions:
    (228 x 152 mm)
    Weight & Pages:
    0.52kg, 264 Pages
    Dimensions:
    Weight & Pages:
    • Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Number Theory, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Tracts in Mathematics (196)
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    Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Number Theory, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Tracts in Mathematics (196)
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    Book description

    Hardy's Z-function, related to the Riemann zeta-function ζ(s), was originally utilised by G. H. Hardy to show that ζ(s) has infinitely many zeros of the form ½+it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on the line ½+it, is perhaps one of the best known and most important open problems in mathematics. Today Hardy's function has many applications; among others it is used for extensive calculations regarding the zeros of ζ(s). This comprehensive account covers many aspects of Z(t), including the distribution of its zeros, Gram points, moments and Mellin transforms. It features an extensive bibliography and end-of-chapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research.

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