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OverviewIn 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. Full Product DetailsAuthor: M.J. Shai Haran (, Technicon-Israel Institute of Technology, Haifa, Israel)Publisher: Oxford University Press Imprint: Oxford University Press Volume: 25 Dimensions: Width: 16.00cm , Height: 1.90cm , Length: 24.20cm Weight: 0.495kg ISBN: 9780198508687ISBN 10: 0198508689 Pages: 256 Publication Date: 20 September 2001 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of Contents0: Introduction 1: The Real Prime 2: The Zeta function and Gamma distribution 3: The Beta distribution 4: The p-adic hyperbolic point of view 5: Some real hyberbolic chains 6: Ramanujan's Garden 7: The q-Gamma and q-Beta chains 8: The real Beta chains 9: Global chains and higher dimensions 10: The Fourier transform 11: The quantum group 12: The Heisenberg group 13: The Riemann Zeta function 14: References / BibliographyReviewsThe book has many interesting ideas ... the book develops a dictionary for moving between the p-adic and real worlds. Zentralblatt Math The book has many interesting ideas ... the book develops a dictionary for moving between the p-adic and real worlds. * Zentralblatt Math * Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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