The Theory Of Hardys Z Function
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| Author | : Aleksandar Ivić |
| Publisher | : Cambridge University Press |
| Total Pages | : 265 |
| Release | : 2012-09-27 |
| Genre | : Mathematics |
| ISBN | : 113978983X |
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 1⁄2+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 1⁄2+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.
| Author | : A. Ivić |
| Publisher | : |
| Total Pages | : 245 |
| Release | : 2013 |
| Genre | : Number theory |
| ISBN | : 9781139779999 |
"This book is an outgrowth of a mini-course held at the Arctic Number Theory School, University of Helsinki, May 18-25, 2011. The central topic is Hardy's function, of great importance in the theory of the Riemann zeta-function. It is named after Godfrey Harold Hardy FRS (1877{1947), who was a prominent English mathematician, well-known for his achievements in number theory and mathematical analysis"--
| Author | : A. Ivić |
| Publisher | : Cambridge University Press |
| Total Pages | : 265 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 1107028833 |
A comprehensive account of Hardy's Z-function, one of the most important functions of analytic number theory.
| Author | : Professor Aleksandar IVI |
| Publisher | : |
| Total Pages | : 266 |
| Release | : 2014-05-14 |
| Genre | : Number theory |
| ISBN | : 9781139776950 |
A comprehensive account of Hardy's Z-function, one of the most important functions of analytic number theory.
| Author | : Jörn Steuding |
| Publisher | : Springer |
| Total Pages | : 320 |
| Release | : 2007-05-26 |
| Genre | : Mathematics |
| ISBN | : 3540448225 |
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
| Author | : S. J. Patterson |
| Publisher | : Cambridge University Press |
| Total Pages | : 172 |
| Release | : 1995-02-02 |
| Genre | : Mathematics |
| ISBN | : 131658335X |
This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number theory. Since then many other classes of 'zeta function' have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.
| Author | : Anatoly A. Karatsuba |
| Publisher | : Walter de Gruyter |
| Total Pages | : 409 |
| Release | : 2011-05-03 |
| Genre | : Mathematics |
| ISBN | : 3110886146 |
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
| Author | : Shigeru Kanemitsu |
| Publisher | : World Scientific |
| Total Pages | : 316 |
| Release | : 2014-12-15 |
| Genre | : Mathematics |
| ISBN | : 9814449628 |
This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.
| Author | : Antanas Laurincikas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 202 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9781402010149 |
This monograph is a generalization of the classic Riemann, and Hurwitz zeta-functions, containing both analytic and probability theory of Lerch zeta-functions.
| Author | : S. J. Patterson |
| Publisher | : Cambridge University Press |
| Total Pages | : 176 |
| Release | : 1995-02-02 |
| Genre | : Mathematics |
| ISBN | : 9780521499057 |
An introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function. It emphasizes central ideas of broad application, avoiding technical results and the customary function-theoretic appro
