The Riemann Hypothesis

A Resource for the Afficionado and Virtuoso Alike

  • Peter Borwein
  • Stephen Choi
  • Brendan Rooney
  • Andrea Weirathmueller
Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Introduction to the Riemann Hypothesis

    1. Front Matter
      Pages 1-1
    2. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 3-8
    3. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 9-27
    4. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 29-36
    5. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 37-44
    6. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 45-54
    7. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 55-60
    8. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 61-67
    9. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 69-72
    10. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 73-79
    11. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 81-90
  3. Original Papers

    1. Front Matter
      Pages 91-91
    2. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 93-160
    3. Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller
      Pages 161-482
  4. Back Matter
    Pages 483-533

About this book

Introduction

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.

Keywords

Calc Microsoft Access Virtuoso algorithms evolution field form mathematics proof selection university

Editors and affiliations

  • Peter Borwein
    • 1
  • Stephen Choi
    • 1
  • Brendan Rooney
    • 2
  • Andrea Weirathmueller
    • 3
  1. 1.Department of Mathematics & StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Simon Fraser UniversityBurnabyCanada
  3. 3.University of Western OntarioFrederictonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-72126-2
  • Copyright Information Springer-Verlag New York 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-72125-5
  • Online ISBN 978-0-387-72126-2
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152