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© 2008

The Riemann Hypothesis

A Resource for the Afficionado and Virtuoso Alike

  • Peter Borwein
  • Stephen Choi
  • Brendan Rooney
  • Andrea Weirathmueller
Book

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

  • Book Title The Riemann Hypothesis
  • Book Subtitle A Resource for the Afficionado and Virtuoso Alike
  • Editors Peter Borwein
    Stephen Choi
    Brendan Rooney
    Andrea Weirathmueller
  • Series Title CMS Books in Mathematics
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-72125-5
  • Softcover ISBN 978-1-4419-2465-0
  • eBook ISBN 978-0-387-72126-2
  • Series ISSN 1613-5237
  • Series E-ISSN 2197-4152
  • Edition Number 1
  • Number of Pages XIV, 533
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    History of Mathematical Sciences
  • Buy this book on publisher's site
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Reviews

From the reviews:

"The Reimann Hypothesis presents itself as fundamentally a collection of well-known papers related to the Reimann Hypothesis, with a long introduction to set the stage. … This may be a useful resource for small libraries … and for those who might like to have copies of the papers in their personal library." (Fernando Q. Gouvêa, MathDL, January, 2008)

"This book is intended as a reference work on the Riemann Hypothesis (RH). … will undoubtedly be extremely useful for anyone making a serious study of the zeta-function, and especially those with an interest in the historical development of the subject. The choice of the material is good, and the discussion is helpful. … anyone working in the area will benefit from a study of them. Overall this is a book which belongs on the shelves of anyone interested in the RH." (Roger Heath-Brown, Zentralblatt MATH, Vol. 1132 (10), 2008)

"Borwein (Simon Fraser Univ.) and others have compiled mostly classic papers contributing to the theory of the distribution of prime numbers. … Summing Up: Recommended. Upper-division undergraduate through researchers/faculty." (D. V. Feldman, CHOICE, Vol. 45 (11), August, 2008)

"This delightfully written book on the Riemann Hypothesis is a welcome addition to the literature. … its structure makes it an ideal choice as a textbook for a reading course on the Riemann zeta function and its applications, especially in classes with students of diverse mathematical backgrounds and abilities. … I thoroughly enjoyed reading this book. … It is a great service to have them collected in one place, and this will increase the number of mathematicians who read them." (Steven Joel Miller, Mathematical Reviews, Issue 2009 k)

“This beautiful book is an in-depth introduction to the Riemann hypothesis, arguably the most famous unsolved problem of mathematics. … the book will also be of interest for anyone with an interest in the history of this result. … For everyone else it is a most valuable resource of information on a fascinating conjecture and a most welcome addition to the literature.” (C. Baxa, Monatshefte für Mathematik, Vol. 160 (3), June, 2010)