Overview
- Contains recent advances and results in number theory
- Collects papers never before published in book form
- Explains the Riemann Hypothesis to someone without a background in complex analysis
Part of the book series: CMS Books in Mathematics (CMSBM)
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Table of contents (12 chapters)
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Front Matter
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Introduction to the Riemann Hypothesis
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Front Matter
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Original Papers
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Front Matter
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Back Matter
Keywords
About this book
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.
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 thehistory 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)
Editors and Affiliations
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
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2008
Hardcover ISBN: 978-0-387-72125-5Published: 30 November 2007
Softcover ISBN: 978-1-4419-2465-0Published: 23 November 2010
eBook ISBN: 978-0-387-72126-2Published: 21 November 2007
Series ISSN: 1613-5237
Series E-ISSN: 2197-4152
Edition Number: 1
Number of Pages: XIV, 533