Theory of Hardy's Z-Function (PDF)
(Sprache: Englisch)
Hardy's Z-function, related to the Riemann zeta-function I (s), was originally utilised by G. H. Hardy to show that I (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...
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Hardy's Z-function, related to the Riemann zeta-function I (s), was originally utilised by G. H. Hardy to show that I (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 I (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.
Bibliographische Angaben
- Autor: Aleksandar Ivic
- 2012, Englisch
- Verlag: Cambridge University Press
- ISBN-10: 1139889524
- ISBN-13: 9781139889520
- Erscheinungsdatum: 27.09.2012
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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Englisch
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