The theory of Hardy's Zfunction
 Author/Creator
 Ivić, A., 1949 author.
 Language
 English.
 Publication
 Cambridge ; New York : Cambridge University Press, 2013.
 Copyright notice
 ©2013
 Physical description
 xvii, 245 pages : illustrations ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 196.
Access
Available online
 dx.doi.org Cambridge Books Online
 proquest.safaribooksonline.com Safari Books Online

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QA241 .I83 2013

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QA241 .I83 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 225238) and indexes.
 Contents

 1. Definition of zeta(s), Z(t) and basic notions 2. The zeros on the critical line 3. The Selberg class of Lfunctions 4. The approximate functional equations for zetak(s) 5. The derivatives of Z(t) 6. Gram points 7. The moments of Hardy's function 8. The primitive of Hardy's function 9. The Mellin transforms of powers of Z(t) 10. Further results on Mk(s)$ and Zk(s) 11. On some problems involving Hardy's function and zeta moments References Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Hardy's Zfunction, related to the Riemann zetafunction zeta(s), was originally utilised by G. H. Hardy to show that zeta(s) has infinitely many zeros of the form 1/2+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 1/2+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 zeta(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 endofchapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research.
(source: Nielsen Book Data)  Supplemental links
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Subjects
 Subject
 Number theory.
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Responsibility
 Aleksandar Ivić, Univerzitet u Beogradu, Serbia.
 Series
 Cambridge tracts in mathematics ; 196
 ISBN
 9781107028838 (hardback)
 1107028833 (hardback)