The Riemann Hypothesis
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The Riemann Hypothesis
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Author : Peter B. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
The Riemann Hypothesis written by Peter B. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
Prime Numbers And The Riemann Hypothesis
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Author : Barry Mazur
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-11
Prime Numbers And The Riemann Hypothesis written by Barry Mazur and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-11 with Mathematics categories.
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Stalking The Riemann Hypothesis
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Author : Daniel Nahum Rockmore
language : en
Publisher: Random House
Release Date : 2011-06-08
Stalking The Riemann Hypothesis written by Daniel Nahum Rockmore and has been published by Random House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-08 with Mathematics categories.
Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.
The Riemann Hypothesis
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Author : Peter Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-21
The Riemann Hypothesis written by Peter Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-21 with Mathematics categories.
This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.
The Riemann Hypothesis And The Distribution Of Prime Numbers
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Author : Naji Arwashan, PhD, PE
language : en
Publisher: Nova Science Publishers
Release Date : 2021-04-15
The Riemann Hypothesis And The Distribution Of Prime Numbers written by Naji Arwashan, PhD, PE and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Mathematics categories.
This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis.
The Riemann Hypothesis
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Author : Karl Sabbagh
language : en
Publisher: Farrar, Straus and Giroux
Release Date : 2004-05-26
The Riemann Hypothesis written by Karl Sabbagh and has been published by Farrar, Straus and Giroux this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-26 with Mathematics categories.
Since 1859, when the shy German mathematician Bernhard Riemann wrote an eight-page article giving a possible answer to a problem that had tormented mathematical minds for centuries, the world's greatest mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann hypothesis. They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995. In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities. Wryly humorous, lively, accessible and comprehensive, The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.
Dr Riemann S Zeros
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Author : Karl Sabbagh
language : en
Publisher: Atlantic Books (UK)
Release Date : 2003
Dr Riemann S Zeros written by Karl Sabbagh and has been published by Atlantic Books (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Biography & Autobiography categories.
Since its inception by Bernard Riemann in 1859, every pure mathematician has longed for a proof for the Riemann hypothesis. Riemann's hypothesis seeks to explain where every single prime number to infinity will occur. This is the story of the quest for the solution.
Riemann S Zeta Function
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Author : Harold M. Edwards
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Riemann S Zeta Function written by Harold M. Edwards and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function
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Author : Samuel W. Gilbert
language : en
Publisher: Riemann hypothesis
Release Date : 2009
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function written by Samuel W. Gilbert and has been published by Riemann hypothesis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function.
The Theory Of The Riemann Zeta Function
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Author : Edward Charles Titchmarsh
language : en
Publisher: Oxford University Press
Release Date : 1986
The Theory Of The Riemann Zeta Function written by Edward Charles Titchmarsh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.