Wow! eBook
The Theory of Hardy's Z-Function: 196
Author(s): Aleksandar Ivić (Author)
- Publisher: Cambridge University Press
- Publication Date: 27 Sept. 2012
- Language: English
- Print length: 264 pages
- ISBN-10: 1107028833
- ISBN-13: 9781107028838
Book Description
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.
