The Mysteries of the Real Prime

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Oxford University Press, 2001 - Mathematics - 240 pages
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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.
  

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Contents

The real prime
1
Global
9
The beta distribution
10
The padic hyperbolic point of view
18
TheH
23
Some real hyperbolic chains
31
The fgamma and Qbeta chains
44
nd higher dimensions
84
oup SUi1
129
ht representation
139
attice model
167
ta function
173
em series connections
181
ein series and the intertwining operator
188
otential connection
203
103
233

sform
98

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About the author (2001)

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

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