The Mysteries of the Real Prime

By: M.J. Shai Haran

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Hardcover | 1 December 2001

At a Glance

Hardcover
256 Pages

Dimensions(cm)
23.39 x 15.6 x 1.6

Hardcover

$177.75

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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.

Industry Reviews

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

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