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Rockmore D. — Stalking the Riemann Hypothesis
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Название: Stalking the Riemann HypothesisАвтор: Rockmore D. Аннотация: In 1859 a German professor named Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the baffling occurrence of prime numbers; coming up with its proof has been the holy grail of mathematicians ever since. In 'Stalking the Riemann Hypothesis, Dan Rockmore, a prominent mathematician in his own right, takes us from Euclid's pondering of the infinitude of the primes through modern efforts to prove the Riemann hypothesis-efforts that astonishingly connect the primes to the statistics of solitaire, chaos theory, and even the mysteries of quantum mechanics. Along the way, he introduces us to the many brilliant and fascinating thinkers who have contributed to this work, from the most famous mathematician of all time, Carl Friedrich Gauss (Riemann's teacher), to the intellectual giants David Hilbert and Freeman Dyson.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 292Добавлена в каталог: 11.03.2008Операции: Положить на полку |
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Schwartz, Laurent 141 Schwingcr, Julian 163 171 237 Scientific American 221 Selberg trace formula 209—211 Selberg zeta function 210—221 Selberg, Atle 141 142 143 147 155 216 217 231 263 Selberg, existence proof of 151 Semiclassical limit 186—231 Semiclassical limit, Berry and 188—189 Semiclassical limit, billiard table analogy see “Billiard tables for physicists” Semiclassical limit, correspondence principle and 187 Semiclassical limit, Hamiltonian matrix and 227—228 Semiclassical limit, life at the 187—188 Semiclassical limit, quantization and 196—200 Semiclassical limit, quantum chaos and 187—190 Semiclassical limit, trace formula and 198 Seminaire Bourbaki 144—145 Sensitive dependence on initial conditions 189—190 198 Sensitive dependence on initial conditions, chaotic dynamical systems and 194—195 208 SETI project 266 Seven bridges of Konigsberg, puzzle of 48—49 Shepp, L. 255 Siegel, Carl Ludwig 64—65 155 Siegel, described 140—141 Siegel, Rademachcr and 147 Siegel, Riemann — Siegel formula and 139—140 Simon, Barry 242 Sinai's table 194 195 198 200 Sinai, Yakov 195 Sine function 160—162 164 Single-valued functions 147 Sinusoids 83 Skewes number 133—134 150 213 Skewes, S. 133 Snaith, Nina 226 262 Sncll, Laurie 234 Snow, C.R 162 Society of Industrial and Applied Mathematics 260 Solitaire 250 253—259 Sorting 248—259 Sound waves 85—86 Spacing distribution 182—184 197—198 Spacing distribution, bulk spectrum 232 Spacings 182 Special functions 238 Spectral geometry 216—227 Spectral lines 172—173 Spectral theory 214 Spectrum, atomic 172 Specular reflection 191 Spin assignment 238—239 Spin states 238—239 Square numbers 10—11 Square pulse 160—161 Square-free numbers 97—99 standing waves 196—197 216 Stanfotd University 177 214 215 221 224 257 Stark, Harold 211 State University of New York at Stony Brook 233 Statistical mechanics 137 Statistical physics 173—175 233 Steepest descent 244 Stieltjes, claimed proof of the Rcimann hypothesis and 95—99 Stieltjes, Thomas 104—105 107 175 177 181 259 Stock market unpredictability 100 102—103 Stoppard, Tom 50 String theory 230 Stuyvesant High School 234 Superposition 83 85 176 Svnehronicity 225 Symplectic matrices 219 Tabor, Michael 197—198 208 Tacoma Narrows bridge 148 Tao, Terrence 265 Taylor, Richard 148 te Riele, Herman 181 Tel Aviv University 218 Teller, Edward 249 tests of significance 226 TeX 257 Theorems 49—51 217 Theoretical computer science 149 Theories 49—50 217 Theory of Numbers (Legendre) 37 66 Theory of Numbers, Fir (Hardy and Wright) 162 Thomas Stieltjes Institute for Mathematics 96 Time 149 Time-limited phenomena 160—161 Time-reversal symmetry 227 Titchmarsh, E.C. 140 Tomonaga, S.-I. 171 237 topology 48—49 Trace formula 198 200 Trace formula, Selberg 209—211 Traces 198 Tracy — Widom distributions 234—241 Tracy — Widom distributions, Deift and 240—246 Tracy, Craig 233—235 260 262 Tracy, described 233—234 Tracy, Ising model and 238—239 Transactions of the American Mathematical Society 148—149 Transcendental numbers 71—72 Transfinite numbers 22—23 Transformation 165—170 229 Transformation, Frobcnius 220 Triangular numbers 11 Trinity College 170 Trivial zeta zeros 88—92 Turing Award 150 253 257 Turing machine 149—151 Turing Test 149—151 Turing, Alan 149—152 Twin Prime Conjecture 265 Twin primes 23—24 Ulam distance 252 Ulam's problem 255—256 Ulam, algorithms and 250—253 Ulam, atomic bomb and 249—250 255 Ulam, described 249 Ulam, Stanislaw 249—253 Uncertainty principle 135 187—188 Unitary matrices 219 University of Arizona 197 University of Birmingham 257 University of Cairo 82 University of California, Berkeley 264 University of California, Davis 234 258 University of California, Los Angeles (UCLA) 265 University of California, Santa Cruz 234 University of Chicago 234 University of Gottingcn 4 59 62 65 66 84 121 122 179 University of Leiden 96 University of Michigan 156 257 University of Pennsylvania 147 148—149 University of Toulouse 96 Update law 239 Vandcrbilt University 265 Veblen, Oswald 155 Vernon, Dale 223 Vershik, A 255 Volkov, A.F. 228 von Koch, Niels 126—127 von Mangoldt, Hans 130 157 von Neumann, John 155 229 249 von Sterneck, R. Daublebsky 103—104 120 259 Wave function 171—172 176—179 216—227 Waves 83—87 Waves, atomic nuclei and 171—172 176—179 Waves, Fourier analysis of 160—161 178 Waves, standing 196—197 Weber's law 34 Wedeniwski, Sebastian 261 266 Weil, Andre 143—147 155 Weil, described 142 144 145 Weil, Eveline 144 Weil, function fields and 143 145—147 220 Weil, Riemann hypothesis and 145—146 Weil, Seminaire Bourbaki and 144—145 Weil, Simonc 144 Wesscl, Caspar 74—75 Weyl, Hermann 146 Widom, described 234 Widom, Harold 233 235 260 Widom, Tracy — Widom distributions 234—246 Wigner, Eugene 174 177 Wiles, Andrew 114 148 261—262 William of Occam 221 Williams, David 152 World War II 140—142 145 149 150 162—163 249 Wright, Wilbur 238 Yohe, J.M. 151 Young tableaux 256 258 Young, Alfred E. 256 Zagier, Don 24 Zeno 53 55 57 58 Zero 3—4 71 Zero, zeta see “Zeta zeros” zeros and ones 16 Zeta zeros 4 86—88 116 see Zeta zeros, computing for 266 Zeta zeros, eigenvalues and 175—185 199—200 210—221 220 225—229 232 Zeta zeros, height or level of 90—91 Zeta zeros, L-series and 110 Zeta zeros, nontrivial 89—92 120 Zeta zeros, quantum chaos and 199 Zeta zeros, random ness of 157—160 Zeta zeros, Riemann hypothesis and 5 88—94 Zeta zeros, trivial 88—92 Zeta-function computer 150 ZetaGrid project 266 Zhou, Xin 243 260
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