The Theory of Hardy's Z-Function | Buch

Cover: 9781107028838 | The Theory of Hardy's Z-Function | Aleksandar Ivi (u. a.) | Buch

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Sprache: Englisch

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Beschreibung

Hardy's Z-function, related to the Riemann zeta-function ¿(s), was originally utilised by G. H. Hardy to show that ¿(s) has infinitely many zeros of the form ¿+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 ¿+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 ¿(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.

Über den Autor

Aleksandar Ivi¿ is a full Professor of Mathematics at the University of Belgrade, Serbia.

Inhaltsverzeichnis

1. Definition of ¿(s), Z(t) and basic notions; 2. The zeros on the critical line; 3. The Selberg class of L-functions; 4. The approximate functional equations for ¿k(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.

Details

Erscheinungsjahr:	2013
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9781107028838
ISBN-10:	1107028833
Sprache:	Englisch
Einband:	Gebunden
Autor:	Ivi, Aleksandar Iviac, A.
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	235 x 157 x 19 mm
Von/Mit:	Aleksandar Ivi (u. a.)
Erscheinungsdatum:	04.07.2013
Gewicht:	0,538 kg