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Rockmore D. Ч Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers
Rockmore D. Ч Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers



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Ќазвание: Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers

јвтор: Rockmore D.

јннотаци€:

For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.
In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2005

 оличество страниц: 304

ƒобавлена в каталог: 10.06.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Moses      93
Mosteller, Fred      224 225
Mount Holyoke      244Ч245
Multivalued function      147Ч148
Nachlass (Riemann)      140
Nahin, Paul      72
Napoleon      81Ч82
Nash, John, Jr.      152Ч153
Natal University      211
Natural logarithm      34Ч35
Natural numbers      7Ч20
Natural numbers as "God given"      7 70 111 137
Natural numbers, composites      12Ч13
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      3Ч6 241 243 261Ч263
Newlands, John      108
Newman, Charlie      262 263
Newton, Isaac      38 48 50 52 82 236
Newton, Isaac, described      46Ч47
Nobel prize      102 150 152 155 163 171 174 257
Nobel Prize, mathematics and      141Ч142
Nobel, Alfred      141Ч142
Non-Euclidean geometry      39 123 201 203Ч205
Noncommutative geometry      230
Noncommutative multiplication      169n 230
Nonconstructive proof      265
Nonlinear differential equations      238
Nonorientable surface      97
Nontrivial zeta zeros      89Ч92
Nonzero      114n
Nuclear weapons      249Ч250 255
NUMBER      259
Number theorists      10
Number theory      10 53 265
Numerical methods      250
Numerosity, pattern of      8Ч10
Occam's razor      221
Odlyzko, Andrew      179n 198 199 218 258 263
Odlyzko, Andrew, described      180Ч181
Odlyzko, Andrew, Dyson Ч Montgomery Ч Odlyzko Law      180Ч185
On the Propagation of Heat in Solid Bodies (Fourier)      81
Operator      177
Operator theory      234
Operator, integral      178Ч179
Operator, zeta zeros and      180 220
Origin of Species, The (Darwin)      63
orthogonal matrices      219
Overfitting data      38 40
p-adic numbers      229Ч230
Pacific Institute of Mathematical Sciences      265
Painleve equations      237 238
Painleve, Paul      237Ч240 246
Painleve, Paul, described      238Ч239
Painleve: transcendants      237Ч240 256
Pair correlations      157Ч160 164
Parallel postulate      203Ч204
Partial differential equation      82
Patience sorting      253Ч254
Patterns      8Ч14
Patterns, figurate numbers and      10Ч11
Patterns, numerosity      8Ч10
Patterns, patterns within      11Ч14
Pavlovskii, V.V.      228
Peer review      148
Perfect number      12
Perfect shuffles      249
Periodic functions      83
Periodic orbit      191 192
permutations      245Ч259
Permutations, computer science and      247Ч249
Petain, Marshal      238
Philosophy      10
Physics      171
Physics, bridge between quantum mechanics and      see semiclassical limit
Physics, physicists      217
Physics, statistical      233
Pi $(\pi)$      58 70Ч71
Planar domains      196
Planck's constant      187Ч188
Planck, Max      187
Plato      13 63
Poe, Edgar Allan      24 236
Poincare conjecture      202
Poincare disk      200Ч209
Poincare disk, chaos in      207Ч209
Poincare, Henri      102
Poincare, Henri, described      202
Point      204n
Poisson process      158Ч160
Poisson, Simeon-Denis      158
Polya Prize      260
Polya Ч Hilbert approach      179Ч180 185 198Ч199 227 232
Polya, George      177Ч180 259Ч260
Polya, George, described      177Ч178
Polya, George, integral operators and      178Ч179
Polynomial      72
Polytechnical School of Delft      95Ч96
Pons, Jean-Louis      40
Population density      41
Poraerance, Carl      264
Poussin, Nicholas      107 119 120
Preprocessing      248
Primal curve      28Ч29 32
Primal waves      86Ч87
Primality tests      15Ч16 264
Prime distribution analyzer (PDA)      76Ч77
Prime distribution analyzer (PDA), Dirichlet's      77 81
Prime distribution analyzer (PDA), Euler s      77 81
Prime distribution analyzer (PDA), Riemannian      77Ч81
Prime factorization      14 20
Prime number theorem      63 91Ч94 95
Prime Number Theorem, Cramer primes and      138Ч139
Prime Number Theorem, Gauss and      42Ч44 69 106 119 120 126 132Ч133 141 185
Prime Number Theorem, Legendre and      35Ч38 69
Prime Number Theorem, mathematically written      36n
Prime Number Theorem, proof of      105 106Ч107 116 118 119 129 139
Prime Number Theorem, statement of      35
Prime numbers, algorithms for checking      264
Prime numbers, as the integral atoms      14Ч15
Prime numbers, asymptotic study of      23Ч30 51 118Ч119
Prime numbers, cardinality of      22Ч23
Prime numbers, composites and      12Ч13
Prime numbers, Cramer      137Ч139 151
Prime numbers, defined      4
Prime numbers, digital cryptography and      17Ч18
Prime numbers, error correction and      16Ч17
Prime numbers, Euclid's proof of the infinitude of      18Ч20 21 24 28 50 51
Prime numbers, first cartographers of      30Ч45
Prime numbers, Gauss and      see Gauss Carl
Prime numbers, Gaussian      112Ч113
Prime numbers, graphs of occurrence of      25Ч29
Prime numbers, harmonic series and      55Ч61
Prime numbers, Hawkins      151Ч152
Prime numbers, infinity of      18Ч20 21 51 59Ч62
Prime numbers, irregular appearance of      23Ч29
Prime numbers, Legendre and      see Legendre Adrie-Marie
Prime numbers, music of      81
Prime numbers, pattern within the pattern      11Ч14
Prime numbers, periodic tables for      59Ч61 107Ч110
Prime numbers, Riemann hypothesis and      see Riemann hypothesis
Prime numbers, search for      14Ч16
Prime numbers, series of reciprocals of      51
Prime numbers, shape of      21Ч29
Prime numbers, slowing occurrence of      41Ч42
Prime numbers, speaking in      16Ч18
Prime numbers, twin      23Ч24
Prime numbers, zeta zeros and      see zeta zeros
Princeton University      154 155 174 195 214 218 219 242Ч243
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      149Ч152
Proof of Riemann hypothesis, search for, Cramer and      136Ч139
Proof of Riemann hypothesis, search for, de la Vallee-Poussin and      107Ч110
Proof of Riemann hypothesis, search for, early twentieth century pursuit of      120Ч127
Proof of Riemann hypothesis, search for, eigenvalues and      see eigenvalues
Proof of Riemann hypothesis, search for, epilogue      263Ч266
Proof of Riemann hypothesis, search for, first steps in      128Ч153
Proof of Riemann hypothesis, search for, Hadamardand      107Ч110
Proof of Riemann hypothesis, search for, Hamiltonian matrix and      227Ч228
Proof of Riemann hypothesis, search for, limits of computation      132Ч134
Proof of Riemann hypothesis, search for, Millennium meeting and      3Ч6 261Ч263
Proof of Riemann hypothesis, search for, Nash and      152Ч153
Proof of Riemann hypothesis, search for, Siegel and      139Ч140
Proof of Riemann hypothesis, search for, Stieltjes and      95Ч99 104Ч105
Proof of Riemann hypothesis, search for, true, false, or neither      134Ч136
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)      10Ч13 54
Pythagoras (Pythagoreans), theorem of      113n 114 115
Quadratic formula      72
Quantization      196Ч200
Quantum chaos      187Ч190
Quantum chaos, basic conjecture of      197Ч200
Quantum chaos, Berry and      187 188Ч189 197Ч198
Quantum chaos, billiard table analogy      see billiard tables for physicists
Quantum chaos, comparison of distributions      222
Quantum chaos, making order out of      213Ч231
Quantum chaos, Sarnak and      217Ч221
Quantum chaos, zeta zeros and      199
Quantum chromodynamics (QCD)      237
Quantum electrodynamics (QED)      163 171 237
Quantum gravity      236Ч237
quantum mechanics      115 136Ч137
Quantum mechanics, classical physics and      171
Quantum mechanics, Planck's constant and      187Ч188
Quantum mechanics, spectral lines and      172Ч173
Quantum mechanics, uncertainty principle and      135 187Ч188
Quantum mechanics, wave function and      171Ч172 176Ч179 see
Rademacher, Hans      147Ч149
RAF Bomber Command      162Ч163
Rains, Eric      258
Random matrices      173Ч175 177Ч180 218
Random Matrices (Mehta)      218 239 244 245
Random matrices, Deift and      244Ч246
Random matrices, RSKand      258Ч259
Random matrices, Tracy Ч Widom distributions and      234Ч241
Random walk      100Ч104 177 178
Random Walk Down Wall Street, A (Malkiel)      102
Randomness      157Ч160
Randomness, understanding through      173Ч175
Rational integers      114
Rational numbers      70 116
Real axis      74
Real numbers      116
Real part of complex numbers      73 74
Reciprocals of logarithms      41Ч42
Reciprocals of Riemann's zeta function      96Ч99
Reeds, Jim      248
Reid, Constance      179 260n
Relative (percentage) error      126Ч127
Relativity theory, general      136 236Ч237
Relativity theory, special      202
Repulsion      160
Rescaling data      158Ч160
Rhind papyrus      246Ч247
Rhind, Henry      246
Rhodes University      242
Richter scale      33Ч34
Riemann hypothesis      88Ч94 125
Riemann hypothesis as "very likely"      91Ч94
Riemann hypothesis as possibly undecidable      134Ч136
Riemann hypothesis for function fields      145Ч147
Riemann hypothesis for L-series      110
Riemann hypothesis, attempts to prove      see proof of Riemann hypothesis search for
Riemann hypothesis, claimed proofs (de Branges)      262Ч263 265Ч266
Riemann hypothesis, complex numbers and      70Ч73
Riemann hypothesis, complex plane and      73Ч76
Riemann hypothesis, defined      4Ч5 47 88Ч91
Riemann hypothesis, equivalence to eigenvalue properties of matrix      179 185
Riemann hypothesis, extended      219
Riemann hypothesis, function zeta zeros and      4 5 88Ч91
Riemann hypothesis, generalized      120Ч121
Riemann hypothesis, incorrect refutation (Rademache)      147Ч149
Riemann hypothesis, Polya Ч Hilbert approach      179Ч180
Riemann hypothesis, publication of      63Ч64
Riemann hypothesis, quest to settle      4Ч6
Riemann hypothesis, raw material for      53
Riemann hypothesis, road to      64Ч69
Riemann hypothesis, web of connections to      259Ч260
Riemann hypothesis, zeta function and      see Ricmann's zeta
Riemann surfaces      147
Riemann Ч Hilbert problems      243Ч244
Riemann Ч Siegel formula      139Ч140 150Ч151
Riemann, Bernhard      4Ч6 63Ч94
Riemann, Bernhard, academic mentors of      45 59 61Ч62 65Ч69 76Ч78
Riemann, Bernhard, death of      65 92Ч93
Riemann, Bernhard, early life      65Ч66
Riemann, Bernhard, formulation of zeta function      80
Riemann, Bernhard, notes of      64Ч65
Riemann, Bernhard, reinvention of space      66Ч69
Riemann, Bernhard, statement of Riemann hypothesis      88Ч91
Riemannian geometry      66Ч69
Riemannian manifold      68
Riemannian prime distribution analyzer      77Ч81
Riemanns zeta function      5
Riemanns Zeta Function (Edwards)      140
Riemanns zeta function, "zoo" of zeta functions and      142Ч143 218 see search
Riemanns zeta function, creation of      76Ч81
Riemanns zeta function, Fourier analysis and      81Ч85
Riemanns zeta function, integral form of      80Ч81 129
Riemanns zeta function, logarithm of      81
Riemanns zeta function, music of the prime powers and      81Ч85
Riemanns zeta function, reciprocal of      96Ч99
Riemanns zeta function, Riemann hypothesis and      88Ч94
Riemanns zeta function, zeros of      85Ч92 119 125Ч126
Riffle shuffling      248
Rising sequence      252Ч259
Robinson Ч Schensted Ч Knuth (RSK) construction      257Ч259
Robinson, Gilbert de Beauregard      257
Rosser, John Barkely      151
Royal Danish Academy      75
Royal Society      150
Rubinstein, Michael      219
Rudnick, Zeev      218Ч219
Rutgers University      233
Saddle point      207
Sarnak, Peter      143 185 227 231 244 260 262
Sarnak, Peter, Cohen and      214Ч216
Sarnak, Peter, described      214 263
Sarnak, Peter, Katz and      219Ч221
Sarnak, Peter, quantum chaos and      217Ч221
Sarnak, Peter, Rudnick and      218Ч219
Sato, M.      237 239Ч240
Saxena, Nitin      264
Scattering theory      242Ч243
Schensted, Craige      257
Schmit, Charles      198
Schoenfeld, Lowell      151
Scholes, Myron      102
Schroedinger, Erwin      179
1 2 3 4
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