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| Ïîèñê ïî óêàçàòåëÿì |
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| Rockmore D. — Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers |
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| Ïðåäìåòíûé óêàçàòåëü |
Moses 93
Mosteller, Fred 224 225
Mount Holyoke 244—245
Multivalued function 147—148
Nachlass (Riemann) 140
Nahin, Paul 72
Napoleon 81—82
Nash, John, Jr. 152—153
Natal University 211
Natural logarithm 34—35
Natural numbers 7—20
Natural numbers as "God given" 7 70 111 137
Natural numbers, composites 12—13
Natural numbers, defined 7
Natural numbers, primes see prime numbers
negative numbers 71
Neudecker, Werner 152
Nevanlinna, R. 145
New York Times 148 149
New York University 3—6 241 243 261—263
Newlands, John 108
Newman, Charlie 262 263
Newton, Isaac 38 48 50 52 82 236
Newton, Isaac, described 46—47
Nobel prize 102 150 152 155 163 171 174 257
Nobel Prize, mathematics and 141—142
Nobel, Alfred 141—142
Non-Euclidean geometry 39 123 201 203—205
Noncommutative geometry 230
Noncommutative multiplication 169n 230
Nonconstructive proof 265
Nonlinear differential equations 238
Nonorientable surface 97
Nontrivial zeta zeros 89—92
Nonzero 114n
Nuclear weapons 249—250 255
NUMBER 259
Number theorists 10
Number theory 10 53 265
Numerical methods 250
Numerosity, pattern of 8—10
Occam's razor 221
Odlyzko, Andrew 179n 198 199 218 258 263
Odlyzko, Andrew, described 180—181
Odlyzko, Andrew, Dyson — Montgomery — Odlyzko Law 180—185
On the Propagation of Heat in Solid Bodies (Fourier) 81
Operator 177
Operator theory 234
Operator, integral 178—179
Operator, zeta zeros and 180 220
Origin of Species, The (Darwin) 63
orthogonal matrices 219
Overfitting data 38 40
p-adic numbers 229—230
Pacific Institute of Mathematical Sciences 265
Painleve equations 237 238
Painleve, Paul 237—240 246
Painleve, Paul, described 238—239
Painleve: transcendants 237—240 256
Pair correlations 157—160 164
Parallel postulate 203—204
Partial differential equation 82
Patience sorting 253—254
Patterns 8—14
Patterns, figurate numbers and 10—11
Patterns, numerosity 8—10
Patterns, patterns within 11—14
Pavlovskii, V.V. 228
Peer review 148
Perfect number 12
Perfect shuffles 249
Periodic functions 83
Periodic orbit 191 192
permutations 245—259
Permutations, computer science and 247—249
Petain, Marshal 238
Philosophy 10
Physics 171
Physics, bridge between quantum mechanics and see semiclassical limit
Physics, physicists 217
Physics, statistical 233
Pi  58 70—71
Planar domains 196
Planck's constant 187—188
Planck, Max 187
Plato 13 63
Poe, Edgar Allan 24 236
Poincare conjecture 202
Poincare disk 200—209
Poincare disk, chaos in 207—209
Poincare, Henri 102
Poincare, Henri, described 202
Point 204n
Poisson process 158—160
Poisson, Simeon-Denis 158
Polya Prize 260
Polya — Hilbert approach 179—180 185 198—199 227 232
Polya, George 177—180 259—260
Polya, George, described 177—178
Polya, George, integral operators and 178—179
Polynomial 72
Polytechnical School of Delft 95—96
Pons, Jean-Louis 40
Population density 41
Poraerance, Carl 264
Poussin, Nicholas 107 119 120
Preprocessing 248
Primal curve 28—29 32
Primal waves 86—87
Primality tests 15—16 264
Prime distribution analyzer (PDA) 76—77
Prime distribution analyzer (PDA), Dirichlet's 77 81
Prime distribution analyzer (PDA), Euler s 77 81
Prime distribution analyzer (PDA), Riemannian 77—81
Prime factorization 14 20
Prime number theorem 63 91—94 95
Prime Number Theorem, Cramer primes and 138—139
Prime Number Theorem, Gauss and 42—44 69 106 119 120 126 132—133 141 185
Prime Number Theorem, Legendre and 35—38 69
Prime Number Theorem, mathematically written 36n
Prime Number Theorem, proof of 105 106—107 116 118 119 129 139
Prime Number Theorem, statement of 35
Prime numbers, algorithms for checking 264
Prime numbers, as the integral atoms 14—15
Prime numbers, asymptotic study of 23—30 51 118—119
Prime numbers, cardinality of 22—23
Prime numbers, composites and 12—13
Prime numbers, Cramer 137—139 151
Prime numbers, defined 4
Prime numbers, digital cryptography and 17—18
Prime numbers, error correction and 16—17
Prime numbers, Euclid's proof of the infinitude of 18—20 21 24 28 50 51
Prime numbers, first cartographers of 30—45
Prime numbers, Gauss and see Gauss Carl
Prime numbers, Gaussian 112—113
Prime numbers, graphs of occurrence of 25—29
Prime numbers, harmonic series and 55—61
Prime numbers, Hawkins 151—152
Prime numbers, infinity of 18—20 21 51 59—62
Prime numbers, irregular appearance of 23—29
Prime numbers, Legendre and see Legendre Adrie-Marie
Prime numbers, music of 81
Prime numbers, pattern within the pattern 11—14
Prime numbers, periodic tables for 59—61 107—110
Prime numbers, Riemann hypothesis and see Riemann hypothesis
Prime numbers, search for 14—16
Prime numbers, series of reciprocals of 51
Prime numbers, shape of 21—29
Prime numbers, slowing occurrence of 41—42
Prime numbers, speaking in 16—18
| Prime numbers, twin 23—24
Prime numbers, zeta zeros and see zeta zeros
Princeton University 154 155 174 195 214 218 219 242—243
Probabilistic number theory 137
Probability theory 223
Proof (Auburn) 50
Proof of Riemann hypothesis, search for 131
Proof of Riemann hypothesis, search for, code breaking and 149—152
Proof of Riemann hypothesis, search for, Cramer and 136—139
Proof of Riemann hypothesis, search for, de la Vallee-Poussin and 107—110
Proof of Riemann hypothesis, search for, early twentieth century pursuit of 120—127
Proof of Riemann hypothesis, search for, eigenvalues and see eigenvalues
Proof of Riemann hypothesis, search for, epilogue 263—266
Proof of Riemann hypothesis, search for, first steps in 128—153
Proof of Riemann hypothesis, search for, Hadamardand 107—110
Proof of Riemann hypothesis, search for, Hamiltonian matrix and 227—228
Proof of Riemann hypothesis, search for, limits of computation 132—134
Proof of Riemann hypothesis, search for, Millennium meeting and 3—6 261—263
Proof of Riemann hypothesis, search for, Nash and 152—153
Proof of Riemann hypothesis, search for, Siegel and 139—140
Proof of Riemann hypothesis, search for, Stieltjes and 95—99 104—105
Proof of Riemann hypothesis, search for, true, false, or neither 134—136
Proof of Riemann hypothesis, search for, two-pronged assault 129
Pseudosphere 207
Ptolemy I 13 50
Purdue University 262 265
Putnam Exam 234
Pythagoras (Pythagoreans) 10—13 54
Pythagoras (Pythagoreans), theorem of 113n 114 115
Quadratic formula 72
Quantization 196—200
Quantum chaos 187—190
Quantum chaos, basic conjecture of 197—200
Quantum chaos, Berry and 187 188—189 197—198
Quantum chaos, billiard table analogy see billiard tables for physicists
Quantum chaos, comparison of distributions 222
Quantum chaos, making order out of 213—231
Quantum chaos, Sarnak and 217—221
Quantum chaos, zeta zeros and 199
Quantum chromodynamics (QCD) 237
Quantum electrodynamics (QED) 163 171 237
Quantum gravity 236—237
quantum mechanics 115 136—137
Quantum mechanics, classical physics and 171
Quantum mechanics, Planck's constant and 187—188
Quantum mechanics, spectral lines and 172—173
Quantum mechanics, uncertainty principle and 135 187—188
Quantum mechanics, wave function and 171—172 176—179 see
Rademacher, Hans 147—149
RAF Bomber Command 162—163
Rains, Eric 258
Random matrices 173—175 177—180 218
Random Matrices (Mehta) 218 239 244 245
Random matrices, Deift and 244—246
Random matrices, RSKand 258—259
Random matrices, Tracy — Widom distributions and 234—241
Random walk 100—104 177 178
Random Walk Down Wall Street, A (Malkiel) 102
Randomness 157—160
Randomness, understanding through 173—175
Rational integers 114
Rational numbers 70 116
Real axis 74
Real numbers 116
Real part of complex numbers 73 74
Reciprocals of logarithms 41—42
Reciprocals of Riemann's zeta function 96—99
Reeds, Jim 248
Reid, Constance 179 260n
Relative (percentage) error 126—127
Relativity theory, general 136 236—237
Relativity theory, special 202
Repulsion 160
Rescaling data 158—160
Rhind papyrus 246—247
Rhind, Henry 246
Rhodes University 242
Richter scale 33—34
Riemann hypothesis 88—94 125
Riemann hypothesis as "very likely" 91—94
Riemann hypothesis as possibly undecidable 134—136
Riemann hypothesis for function fields 145—147
Riemann hypothesis for L-series 110
Riemann hypothesis, attempts to prove see proof of Riemann hypothesis search for
Riemann hypothesis, claimed proofs (de Branges) 262—263 265—266
Riemann hypothesis, complex numbers and 70—73
Riemann hypothesis, complex plane and 73—76
Riemann hypothesis, defined 4—5 47 88—91
Riemann hypothesis, equivalence to eigenvalue properties of matrix 179 185
Riemann hypothesis, extended 219
Riemann hypothesis, function zeta zeros and 4 5 88—91
Riemann hypothesis, generalized 120—121
Riemann hypothesis, incorrect refutation (Rademache) 147—149
Riemann hypothesis, Polya — Hilbert approach 179—180
Riemann hypothesis, publication of 63—64
Riemann hypothesis, quest to settle 4—6
Riemann hypothesis, raw material for 53
Riemann hypothesis, road to 64—69
Riemann hypothesis, web of connections to 259—260
Riemann hypothesis, zeta function and see Ricmann's zeta
Riemann surfaces 147
Riemann — Hilbert problems 243—244
Riemann — Siegel formula 139—140 150—151
Riemann, Bernhard 4—6 63—94
Riemann, Bernhard, academic mentors of 45 59 61—62 65—69 76—78
Riemann, Bernhard, death of 65 92—93
Riemann, Bernhard, early life 65—66
Riemann, Bernhard, formulation of zeta function 80
Riemann, Bernhard, notes of 64—65
Riemann, Bernhard, reinvention of space 66—69
Riemann, Bernhard, statement of Riemann hypothesis 88—91
Riemannian geometry 66—69
Riemannian manifold 68
Riemannian prime distribution analyzer 77—81
Riemanns zeta function 5
Riemanns Zeta Function (Edwards) 140
Riemanns zeta function, "zoo" of zeta functions and 142—143 218 see search
Riemanns zeta function, creation of 76—81
Riemanns zeta function, Fourier analysis and 81—85
Riemanns zeta function, integral form of 80—81 129
Riemanns zeta function, logarithm of 81
Riemanns zeta function, music of the prime powers and 81—85
Riemanns zeta function, reciprocal of 96—99
Riemanns zeta function, Riemann hypothesis and 88—94
Riemanns zeta function, zeros of 85—92 119 125—126
Riffle shuffling 248
Rising sequence 252—259
Robinson — Schensted — Knuth (RSK) construction 257—259
Robinson, Gilbert de Beauregard 257
Rosser, John Barkely 151
Royal Danish Academy 75
Royal Society 150
Rubinstein, Michael 219
Rudnick, Zeev 218—219
Rutgers University 233
Saddle point 207
Sarnak, Peter 143 185 227 231 244 260 262
Sarnak, Peter, Cohen and 214—216
Sarnak, Peter, described 214 263
Sarnak, Peter, Katz and 219—221
Sarnak, Peter, quantum chaos and 217—221
Sarnak, Peter, Rudnick and 218—219
Sato, M. 237 239—240
Saxena, Nitin 264
Scattering theory 242—243
Schensted, Craige 257
Schmit, Charles 198
Schoenfeld, Lowell 151
Scholes, Myron 102
Schroedinger, Erwin 179
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