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The real prime | p. 1 |
Algebra and geometry | p. 1 |
The real prime | p. 3 |
The mystery | p. 4 |
The zeta function and gamma distribution | p. 6 |
The local zeta function | p. 6 |
The gamma distribution | p. 7 |
Remarks on global theory | p. 8 |
The beta distribution | p. 10 |
Phase space | p. 10 |
The beta distribution | p. 11 |
Special values | p. 13 |
Remarks on the global theory | p. 15 |
The p-adic hyperbolic point of view | p. 17 |
Chains and trees | p. 17 |
The p-adic gamma chain | p. 21 |
The p-adic symmetric beta chain | p. 24 |
The p-adic beta chain | p. 28 |
Some real hyperbolic chains | p. 31 |
The hyperbolic plane | p. 31 |
N-adic expansion | p. 31 |
Continued fraction expansion | p. 31 |
Ramanujan's garden | p. 34 |
The q-zeta function | p. 34 |
Elliptic curves | p. 36 |
q-series | p. 37 |
The q-gamma and q-beta chains | p. 44 |
The q-gamma chain | p. 44 |
The q-beta chains | p. 47 |
The Heisenberg relation and special basis | p. 52 |
The real beta chains | p. 65 |
The beta chain | p. 65 |
The Heisenberg relations and the special basis | p. 67 |
The real units | p. 76 |
Global 'chains' and higher dimensions | p. 84 |
Restricted direct products of chains | p. 84 |
Higher dimensional beta chains | p. 87 |
The Fourier transform | p. 98 |
The Tate distribution and the beta function at imaginary argument | p. 98 |
The Fourier--Bessel transform | p. 101 |
Symmetric convolution | p. 103 |
The basic basis and the Laguerre basis | p. 105 |
The beta measure | p. 110 |
The pure gamma basis and the cut-off basis | p. 112 |
The pure beta basis | p. 122 |
The Askey--Wilson polynomials | p. 124 |
The quantum group SU (1,1) | p. 129 |
The quantum enveloping algebra U[subscript q] | p. 129 |
Highest weight representation | p. 131 |
The Hopf algebra structure | p. 135 |
The universal R-matrix | p. 139 |
The Heisenberg group | p. 142 |
The Heisenberg group and its fundamental representation | p. 142 |
Twisted convolution and multiplication | p. 145 |
Matrix coefficients | p. 147 |
The local lattice model | p. 149 |
Special basis | p. 154 |
The global lattice model | p. 161 |
Automorphic forms on the Heisenberg group | p. 167 |
The Riemann zeta function | p. 173 |
The Riemann zeta function and the theta function | p. 173 |
The explicit sums | p. 176 |
The Eisenstein series connections | p. 181 |
The Eisenstein series and the intertwining operator | p. 188 |
The Riesz potential connection | p. 207 |
Bibliography | p. 226 |
Index | p. 233 |
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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.