The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (CMS Books in Mathematics) [Hardcover]

Peter Borwein (Editor), Stephen Choi (Editor), Brendan Rooney (Editor), Andrea Weirathmueller (Editor)

Book Description

ISBN-10: 0387721258 | ISBN-13: 978-0387721255 | Publication Date: November 30, 2007 | Edition: 1

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.

Editorial Reviews

Review

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)

From the Back Cover

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.

Product Details

• Hardcover: 552 pages
• Publisher: Springer; 1 edition (November 30, 2007)
• Language: English
• ISBN-10: 0387721258
• ISBN-13: 978-0387721255
• Product Dimensions: 9.3 x 6.4 x 1.2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,312,240 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

1 of 1 people found the following review helpful:

5.0 out of 5 stars The best one-stop Riemann shop for now, October 26, 2011

By 

R. Cook "heycarnut" (Bay Are, CA United States) - See all my reviews
(REAL NAME)   

This review is from: The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (CMS Books in Mathematics) (Paperback)

For a practitioner looking for a quick road-map, or for a graduate student looking for an excellent overview, this is the best I've seen. It is most assuredly *not* one of the titles directed at the lay audience, though it is certainly approachable to the very bright, mathematically inclined of that audience. This is more of a "source book" of theoretical overview, ramifications, recent results, backed by reprints of original papers. A recommended addition to the library of any mathematician.

7 of 13 people found the following review helpful:

4.0 out of 5 stars Not all papers are in English, November 23, 2009

By 

Grant Moule (Australia) - See all my reviews
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This review is from: The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (CMS Books in Mathematics) (Hardcover)

I enjoyed reading the book which gave me more appreciation of how some of the important results relating the to Riemann Hypothesis are derived. However, I was disappointed that not all of the included reference papers were in English. I think these could have all been translated.