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The theory of Hardy's Z-function

Ivic, A., (1949-)

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The theory of Hardy's Z-function

Record Type:	Electronic resources : Monograph/item
Title/Author:	The theory of Hardy's Z-function/ Aleksandar Ivic, Univerzitet u Beogradu, Serbia.
Author:	Ivic, A.,
Published:	Cambridge :Cambridge University Press, : 2013.,
Description:	xvii, 245 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	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.
Subject:	Number theory. -
Online resource:	https://doi.org/10.1017/CBO9781139236973
ISBN:	9781139236973

The theory of Hardy's Z-function
Ivic, A.,1949-

The theory of Hardy's Z-function[electronic resource] /Aleksandar Ivic, Univerzitet u Beogradu, Serbia. - Cambridge :Cambridge University Press,2013. - xvii, 245 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;196. - Cambridge tracts in mathematics ;196..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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.

ISBN: 9781139236973Subjects--Topical Terms:

515832
Number theory.

LC Class. No.: QA241 / .I83 2013

Dewey Class. No.: 512.7

The theory of Hardy's Z-function
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245 1 4 $a The theory of Hardy's Z-function $h [electronic resource] / $c Aleksandar Ivic, Univerzitet u Beogradu, Serbia.
260 $a Cambridge : $b Cambridge University Press, $c 2013.
300 $a xvii, 245 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 196
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Number theory. $3 515832
830 0 $a Cambridge tracts in mathematics ; $v 196. $3 3470544
856 4 0 $u https://doi.org/10.1017/CBO9781139236973