The theory of Hardy's Z-function / Aleksandar Ivić, Univerzitet u Beogradu, Serbia.

Format:

Book

Author/Creator:

Ivić, A., 1949- author.

Series:

Cambridge tracts in mathematics ; 196.

Cambridge tracts in mathematics ; 196

Language:

English

Subjects (All):

Number theory.

Physical Description:

1 online resource (xvii, 245 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

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

Includes bibliographical references and indexes.

ISBN:

1-139-79435-3

1-139-88952-4

1-139-77999-0

1-139-23697-0

1-139-78385-8

1-139-78298-3

1-139-77695-9

1-283-71476-0

1-139-77847-1

OCLC:

833769574