The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (CMS Books in Mathematics) 2008th Edition by Peter Borwein (PDF)

Description

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.

User’s Reviews

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)“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) 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐If you are interested in the Riemann Hypothesis and the Riemann Zeta function this book should answer all of your questions.

⭐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.

⭐The author simply pasted different articles one after the other taking absolutely no care whether the format is consistant or not.

⭐Suppose you want to solve the Riemann hypothesis (you bet) or just want to know more about it (hoping for option one), then this book might be what you need. This book contains all the original papers that have contributed something to the advance of the solution to this nasty math problem. I think it helps a lot if you are a seasoned math pro. In that case you might understand all of this. I myself am a stumbling amateur looking in amazement at the work done by Riemann, Chebychev, Hadmard, de lav Vallée Poussin, Hardy, Littlewood, Weil, Turan, Selberg, Erdos, Skewes, Haselgrove, Montgomery, Newman, Korevaar, Dabousi, Hildebrand, Goldston and finall Agawal, Kayal and Saxena.In this book I think nobody in the entire story is missing. There is enough introductionary material to get the appetite going too. But this book contains some very sophisticated math, and I doubt that mastering this book could take less than a year.I myself take it up every now and then to how much I grasp in the meantime.A warning to the wise : the papers at the end of the book are in the original language they were published (the repro is not perfect but generally satisfactory), which means you will meet French, English and German. The original Riemann paper is reproduced in German in his original handwriting but is unfortunately unreadable for mere mortals (not because of the math but because of the handwriting).

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