東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

The theory of Hardy's Z-function

Ivic, A., (1949-)

FindBook

Google Book

Amazon

博客來

The theory of Hardy's Z-function

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The theory of Hardy's Z-function/ Aleksandar Ivic, Univerzitet u Beogradu, Serbia.
作者:	Ivic, A.,
出版者:	Cambridge :Cambridge University Press, : 2013.,
面頁冊數:	xvii, 245 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Number theory. -
電子資源:	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
LDR:02147nmm a2200277 a 4500 001 2227231
003 UkCbUP
005 20151005020621.0
006 m d
007 cr nn 008maaau
008 210414s2013 enk o 1 0 eng d
020 $a 9781139236973 $q (electronic bk.)
020 $a 9781107028838 $q (hardback)
035 $a CR9781139236973
040 $a UkCbUP $b eng $c UkCbUP $d GP
041 0 $a eng
050 4 $a QA241 $b .I83 2013
082 0 4 $a 512.7 $2 23
090 $a QA241 $b .I95 2013
100 1 $a Ivic, A., $d 1949- $3 3470543
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