Format:
1 Online-Ressource (xvii, 245 pages)
,
digital, PDF file(s).
ISBN:
9781139236973
Series Statement:
Cambridge tracts in mathematics 196
Content:
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.
Content:
Definition of (s), Z(t) and basic notions -- Zeros on the critical line -- Selberg class of L-functions -- Approximate functional equations for k(s) -- Derivatives of Z(t) -- Gram points -- Moments of Hardy's function -- Primitive of Hardy's function -- Mellin transforms of powers of Z(t) -- Further results on Mk(s) and Zk(s) -- On some problems involving Hardy's function
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9781107028838
Additional Edition:
ISBN 9781107028838
Additional Edition:
Erscheint auch als Ivić, Aleksandar, 1949 - 2020 The theory of Hardy's Z-function Cambridge [u.a.] : Cambridge Univ. Press, 2013 ISBN 9781107028838
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781107028838
Language:
English
Subjects:
Mathematics
Keywords:
Zahlentheorie
DOI:
10.1017/CBO9781139236973
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