Mysteries of the Real Prime

Name: Mysteries of the Real Prime
Price: 196.94 USD
Availability: InStock
ISBN: 9780198508687

ISBN-10: 0198508689

ISBN-13: 9780198508687

Edition: 2001

Authors: M. J. Shai Haran

List price: $190.00

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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…

Book details

List price: $190.00
Copyright year: 2001
Publisher: London Mathematical Society
Publication date: 12/6/2001
Binding: Hardcover
Pages: 256
Size: 6.30" wide x 9.53" long x 0.75" tall
Weight: 1.078
Language: English




The real prime



Algebra and geometry



The real prime



The mystery



The zeta function and gamma distribution



The local zeta function



The gamma distribution



Remarks on global theory



The beta distribution



Phase space



The beta distribution



Special values



Remarks on the global theory



The p-adic hyperbolic point of view



Chains and trees



The p-adic gamma chain



The p-adic symmetric beta chain



The p-adic beta chain



Some real hyperbolic chains



The hyperbolic plane



N-adic expansion



Continued fraction expansion



Ramanujan's garden



The q-zeta function



Elliptic curves



q-series



The q-gamma and q-beta chains



The q-gamma chain



The q-beta chains



The Heisenberg relation and special basis



The real beta chains



The beta chain



The Heisenberg relations and the special basis



The real units



Global 'chains' and higher dimensions



Restricted direct products of chains



Higher dimensional beta chains



The Fourier transform



The Tate distribution and the beta function at imaginary argument



The Fourier--Bessel transform



Symmetric convolution



The basic basis and the Laguerre basis



The beta measure



The pure gamma basis and the cut-off basis



The pure beta basis



The Askey--Wilson polynomials



The quantum group SU (1,1)



The quantum enveloping algebra U[subscript q]



Highest weight representation



The Hopf algebra structure



The universal R-matrix



The Heisenberg group



The Heisenberg group and its fundamental representation



Twisted convolution and multiplication



Matrix coefficients



The local lattice model



Special basis



The global lattice model



Automorphic forms on the Heisenberg group



The Riemann zeta function



The Riemann zeta function and the theta function



The explicit sums



The Eisenstein series connections



The Eisenstein series and the intertwining operator



The Riesz potential connection


Bibliography


Index