The Mysteries of the Real Prime

Hardcover | February 15, 2002

byM.J. Shai Haran

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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 Heisenberggroup, 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 andthe real theory by constructing a theory of quantum orthagonal polynomials.

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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 m...

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

other books by M.J. Shai Haran

Format:HardcoverDimensions:254 pages, 9.21 × 6.14 × 0.75 inPublished:February 15, 2002Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198508689

ISBN - 13:9780198508687

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Table of Contents

0. Introduction1. The Real Prime2. The Zeta function and Gamma distribution3. The Beta distribution4. The p-adic hyperbolic point of view5. Some real hyberbolic chains6. Ramanujan's Garden7. The q-Gamma and q-Beta chains8. The real Beta chains9. Global "chains" and higher dimensions10. The Fourier transform11. The quantum group12. The Heisenberg group13. The Riemann Zeta function14. References / Bibliography