The Mysteries of the Real Prime (Oxford Science Publications) [Hardcover]

M.J. Shai Haran (Author)

Book Description

ISBN-10: 0198508689 | ISBN-13: 978-0198508687 | Publication Date: December 6, 2001

In this important and original monograph, useful for both academic and professional researchers and students of mathematics and physics, the author describes his work on the Riemann zeta function and its adelic interpretation. It provides an original point of view, bringing new, highly useful dictionaries between different fields of mathematics. It develops an arithmetical approach to the continuum of real numbers and unifies many areas of mathematics including: Markov Chains, q-series, Elliptic curves, the Heisenberg group, quantum groups, and special functions (such as the Gamma, Beta, Zeta, theta, Bessel functions, the Askey-Wilson and the classical orthagonal polynomials) The text discusses real numbers from a p-adic point of view, first mooted by Araeklov. It includes original work on coherent theory, with implications for number theory and uses ideas from probability theory including Markov chains and noncommutative geometry which unifies the p-adic theory and the real theory by constructing a theory of quantum orthagonal polynomials.

Editorial Reviews

Review

"The problem is not with the primes themselves, explains Haran (mathematics, Israel Institute of Technology): the primes are just a set and, to put as diplomatic spin on it as objective science permits, there is not much interesting to say about them as such. The problems arise--and some interesting problems indeed--when the primes begin interacting with other sets. He takes the set of real numbers, as one of many completions of the rational numbers, and searches for the secret of the real prime."--SciTech Book News

About the Author

M.J. Shai Haran is at Technicon-Israel Institute of Technology, Haifa, Israel.

Product Details

• Hardcover: 256 pages
• Publisher: Oxford University Press, USA (December 6, 2001)
• Language: English
• ISBN-10: 0198508689
• ISBN-13: 978-0198508687
• Product Dimensions: 9.3 x 6.1 x 0.8 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #4,324,324 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

1 of 4 people found the following review helpful:

5.0 out of 5 stars Incredible implications for physics and mathematics, April 16, 2003

By A Customer

This review is from: The Mysteries of the Real Prime (Oxford Science Publications) (Hardcover)

At first it seemed this book was [spendy] but once I bought it I had no regrets. Mastering the material, means that one gets a glimpse at the potential exquisite simplicity of the p-adics. You also get a real sense that the proof of the greatest problem of all - the Riemann Hypothesis - is not far away if Haran's philosophy is pursued just one step further....