# The Riemann Hypothesis

Mathematics is full of unsolved problems and other mysteries, but none more important and intriguing than the Riemann hypothesis. Baffling the greatest minds for more than a hundred and fifty years, the Riemann hypothesis is at the very ...

Author: Roland van der Veen

Publisher: The Mathematical Association of America

ISBN: 9780883856505

Category: Mathematics

Page: 154

View: 824

This book introduces interested readers to one of the most famous and difficult open problems in mathematics: the Riemann Hypothesis. Finding a proof will not only make you famous, but also earns you a one million dollar prize. The book originated from an online internet course at the University of Amsterdam for mathematically talented secondary school students. Its aim was to bring them into contact with challenging university level mathematics and show them why the Riemann Hypothesis is such an important problem in mathematics. After taking this course, many participants decided to study in mathematics at university.

# The Riemann Hypothesis

The Riemann hypothesis is equivalent to ( ξ(s)ξ(s) ) >0. Continuing to work with ξ(s), we define λn as 1 dn λn := (n−1)! dsn (sn−1 logξ(s)). Now we can state an equivalence relating the Riemann hypothesis to the value of λn.

Author: Peter Borwein

Publisher: Springer Science & Business Media

ISBN: 9780387721262

Category: Mathematics

Page: 533

View: 131

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.

# Stalking The Riemann Hypothesis

the world of our usual primes, assuming that the Riemann hypothesis turned out to be true. So, the Riemann hypothesis was looking like a pretty good bet. EVIDENCE ACCUMULATES In 1932 Carl Ludwig Siegel (see Chapter 6), ...

Author: Daniel Nahum Rockmore

Publisher: Random House

ISBN: 9781446483626

Category: Mathematics

Page: 304

View: 159

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.

# Equivalents of the Riemann Hypothesis

A. Chang, D. Mehrle, S. J. Miller, T. Reiter, J. Stahl and D. Yott, Newman's conjecture in function fields, ... J. Cislo and M. Wolf, Equivalence of Riesz and B ́aez-Duarte criterion for the Riemann hypothesis, Preprint, 2006.

Author: Kevin Broughan

Publisher: Cambridge University Press

ISBN: 9781107197121

Category: Mathematics

Page: 488

View: 974

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

# Casimir Force Casimir Operators and the Riemann Hypothesis

For some further interesting comments on these matters,the origin of Riemann's paper and the contributions of Malmstén and Schlömilch to the theory of the Riemann zeta function see [23, pp. 8–9]. Riemann's paper establishes a direct ...

Author: Gerrit Dijk

Publisher: Walter de Gruyter

ISBN: 9783110226133

Category: Mathematics

Page: 294

View: 169

This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry

# Prime Numbers and the Riemann Hypothesis

PRIME NUMBERS AND THE RIEMANN HYPOTHESIS Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis ...

Author: Barry Mazur

Publisher: Cambridge University Press

ISBN: 9781107101920

Category: Mathematics

Page: 150

View: 495

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

# Equivalents of the Riemann Hypothesis Volume 2 Analytic Equivalents

A. Chang, D. Mehrle, S. J. Miller, T. Reiter, J. Stahl and D. Yott, Newman's conjecture in function fields, ... J. Cislo and M. Wolf, Equivalence of Riesz and B ́aez-Duarte criterion for the Riemann hypothesis, Preprint, 2006.

Author: Kevin Broughan

Publisher: Cambridge University Press

ISBN: 9781108187022

Category: Mathematics

Page:

View: 314

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

# The Riemann Hypothesis in Characteristic p in Historical Perspective

In each of Artin's cases, about 40 in number, he verifies numerically the Riemann hypothesis, by computing the coefficient σ1 and discussing the nontrivial zeros of the corresponding L-polynomial. Furthermore, Artin remarks (without ...

Author: Peter Roquette

Publisher: Springer

ISBN: 9783319990675

Category: Mathematics

Page: 235

View: 589

This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.

# Equivalents of the Riemann Hypothesis Volume 1 Arithmetic Equivalents

K. Sabbagh, The Riemann Hypothesis, Farrar, Straus and Giroux, 2003. B. Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Springer, 2001. J. S ́andor, D. S. Mitrinovi ́c and B. Crstici, ...

Author: Kevin Broughan

Publisher: Cambridge University Press

ISBN: 9781108195416

Category: Mathematics

Page:

View: 186

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

# The Riemann Hypothesis and the Distribution of Prime Numbers

the Riemann Hypothesis as one of its seven millennial problems and allocated a million-dollar prize for the proof of any of them. The Riemann Hypothesis is considered by many accounts the single most important and difficult question in ...

Author: Naji Arwashan, PhD, PE

Publisher: Nova Science Publishers

ISBN: 9781536194227

Category: Mathematics

Page: 219

View: 545

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.