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| Ïîèñê ïî óêàçàòåëÿì |
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| Derbyshire J. — Prime Obsession: Bernhard Riemann and the greatest unsolved problem in mathematics |
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| Ïðåäìåòíûé óêàçàòåëü |
Open form 64
Operator theory 265 271—279 351 see
Operators 273—274 386 see
Order of a zero 385
p-adic numbers 173 319—320
Pair correlation function 287 288 290—291
Paphnutius, Bishop 122—123
Paris Academy of Sciences 58 160
Particle Physics 198 280—281 295
Pascal, Blaise 371
Patterson, Samuel J. 217 385
Paul I, Emperor of Russia 121
Periodic terms 328 330—333 339—340 341
Perturbation theory 351
Peter the Great, Emperor of Russia 56—57 58 pl.
Petsinis, Tom 369
Picard's theorem 389—390
Picard, Emile 165 389—390
Picquart, George 162 164
Pietists 187
Planck's constant 316
PNT see "Prime Number Theorem"
Poincare, Henri 92 159 314 377
Point at infinity 214
Poisson distribution 387
Poisson, Simeon-Denis 92 93
Polya, George 193 197 228 277 325 352 377—378 380 pl.
Polynomial, characteristic of a matrix 272—273
Polynomial, function 37 331—332
Polynomial, zero of 173
Polytopes 196 378
Popular Front 164
Power functions, derivatives of 110
Powers, complex 178 202—203 204—205
Powers, fractional 66—67 68
Powers, graphing 68 73
Powers, irrational 67
Powers, rules 65—68 69 71—72
Powers, zero 65 66
Prime counting function 38 153—154 160 297 298 299
Prime Number Theorem (PNT), calculus and 106—113
Prime Number Theorem (PNT), Chebyshev and 123—124
Prime Number Theorem (PNT), consequences of 45—47 323—324 359—360
Prime Number Theorem (PNT), equivalents 47
Prime Number Theorem (PNT), expressions 45 116
Prime Number Theorem (PNT), first published work 54
Prime Number Theorem (PNT), Gauss and 51 53—54
Prime Number Theorem (PNT), graph 117
Prime Number Theorem (PNT), improved version 116
Prime Number Theorem (PNT), log integral function and 113—117
Prime Number Theorem (PNT), logarithmic sense 45—46
Prime Number Theorem (PNT), proofs 124—125 153—155 159—160 190 198 233—234 237 356
Prime numbers and zeros of zeta function 154
Prime numbers, Chebyshev bias 125—126
Prime numbers, defined 32
Prime numbers, frequency of see "Prime Number Theorem"
Prime numbers, infinity of 34 95—97 105
Prime numbers, probabilist model for distribution of 198
Prime numbers, series of reciprocals of 154
Prime numbers, sieve method for finding 100—101
Prime numbers, tables 33 153—154
Prime numbers, thinning out of 34—35
Princeton University 245
Principia Mathematica (Whitehead and Russell) 89 225 361 391
Product sign ( ) 105
Proper factor 32
Proper fraction 171
Psychology of Invention in the Mathematical Field (Hadamard) 165 359
Pushkin, Alexander 122
Pythagoras of Samos 175 367 379
Pythagoras's theorem 180
Quantum dynamics 291—292
Quantum factor 316
Quantum physics 313 315—317
Quasi-Riemann Hypothesis xiv
Ramanujan, Srinivasa 227—228
random matrix 282—287 386 403
Random numbers, Gaussian-normal 283
Random numbers, spacings between 285—286
Random walk 250
Rational functions 268—269 332
Rational numbers 171 172 173 175 179 319
Real axis 180
Real line 178—180
Real numbers 171 172 173 176 178 188
Regular Polytopes (Coxeter) 196
Reid, Constance 186 188
Relative error 234—235
Relativity, general theory of 128—129 130 318
Rellich, Franz 383
Renaissance 175
Repulsion effect 284 285—286
Rh see "Riemann Hypothesis"
Riemann Hypothesis and zeta function 136 137
Riemann Hypothesis in song 393—403
Riemann Hypothesis, "Hypothesis" vs. "Conjecture", "Theorem", etc. 386
Riemann Hypothesis, algebraic thread 197
Riemann Hypothesis, analytic number theory and 86
Riemann Hypothesis, computational thread 197
Riemann Hypothesis, consequences of 358—360
Riemann Hypothesis, elementary math xii—xiii
Riemann Hypothesis, error term 190 234—235 236—237 244
Riemann Hypothesis, geometrically stated 190
Riemann Hypothesis, harmonic series and 12
Riemann Hypothesis, Hilbert's eighth problem 189—190 244 324
Riemann Hypothesis, mathematicians' fascination with 156—157 186—187 188 189—190 196—198 200 232
Riemann Hypothesis, physical thread 197—198 271—272
Riemann Hypothesis, presentation at Berlin Academy meeting ix—x 31
Riemann Hypothesis, prize for proofs disproof xi 154 354
Riemann Hypothesis, prospects for proofs disproof 354—358
Riemann Hypothesis, statements of xi—xii 77 137 191
Riemann Hypothesis, Stieltjes' lost proof 154 160 161
Riemann integral 127
Riemann operators 312 316—319 320—321
Riemann surfaces 121 209—210
Riemann zeta function see "Zeta function"
Riemann — Siegel formula 256—257 262 263—264 292 316
Riemann's Zeta Function (Edwards) 153 217 375 384
Riemann, Bernhard 2
Riemann, Bernhard and analytic number theory 97—98
Riemann, Bernhard and theory of many-valued functions 43
Riemann, Bernhard on error term's big oh 244—245 381
Riemann, Bernhard on error term's sign 235
Riemann, Bernhard, "breakout year" 31
Riemann, Bernhard, academic career 19 30—31 131—132 134 135
Riemann, Bernhard, bereavements xiv—xv 23 133 134
Riemann, Bernhard, Berlin Academy ix 119 135
Riemann, Bernhard, Collected Works 27 29 131 366
Riemann, Bernhard, death 362—364
Riemann, Bernhard, doctorate and habilitation 119—121 126 127—129 130
Riemann, Bernhard, early life and home environment 22—23
Riemann, Bernhard, friends and colleagues 27—28 29 119 120
Riemann, Bernhard, health problems xiv 23—24 28 133
Riemann, Bernhard, honors and awards 31 135
Riemann, Bernhard, intellectual abilities and interests 129—130 131 152 194
Riemann, Bernhard, lecturing style 132
Riemann, Bernhard, lunar crater named after 374
Riemann, Bernhard, marriage and family 31 362
Riemann, Bernhard, mentors 94—95 98 119 126—127 133
Riemann, Bernhard, papers and published works 29 30—31 127—128 131 133 135 151
Riemann, Bernhard, personal characteristics 27—29 127
Riemann, Bernhard, poverty xv 119—120
Riemann, Bernhard, religious faith 28 127 363
Riemann, Bernhard, schooling and scholarship 24—25 27 29 30—31
Riemann, Bernhard, social awkwardness xiv—xv 133
Riemann, Clara 133
Riemann, Elise (nee Koch) 31 362 363—364
Riemann, Friedrich Bernhard (father) 22—23
Riemann, Ida (daughter) 362 364
Riemann, Ida (sister) 22 31 363—364
| Riemann, Marie (sister) 134
Riemann, Wilhelm (brother) 134
Ring 267—268
Rivat, Joel 380
Romantic movement 30 92 118
Rosser, J.Barkley 258
Rubinstein, Michael 380
Rule of signs 42 367—368
Ruler exercises 10—15
Russell, Bertrand 225 226 360—361
Russia, intellectual life in 55—57 58—59 60—61 98 120—122
Rutherford, Ernest 280
S function 358 396
Sarnak, Peter 245 278 352 380 387 388
Scherrer, Paul 185
Schilling, Carl David 364
Schneider, Theodor 354
Schoenhage, Arnold 263—264
Schogt, Philibert 161
Schroedinger's wave equation 313
Schwartz, Hermann 363—364
Seattle conference on the Riemann Hypothesis 257 352 355
Selberg, Atle 125 198 288 352 358 374 376 384 pl.
Semiclassical dynamical system 316
Sequence of partial sums 17
Sequence, defined 16
Sequence, series contrasted 16—17
Series see also "Harmonic series"
Series of reciprocal squares 64—65
Series, Basel 63—64
Series, convergent 11—15 79
Series, defined 8
Series, divergent 9—10 81 139
Series, infinite 59 63 75
Series, ruler exercises 10—15
Series, sequences contrasted 16—17
Serre, Jean-Pierre 372 384
Set theory 18 88
Seven Years War 60
Siegel, Carl 256—257 263—264 383 pl.
Sieve of Eratosthenes 100—101 102—104 138
Sine function 147 332
Skewes' number 236
Skewes, Samuel 236
Snaith, Nina xiv
Snowflake curve 381
Society of German Scientists and Physicians 252
Sommerfeld, Arnold 256
Sophia Dorothea (mother of Frederick the Great) 60
Sorbonne 159 188 225
Sorcerer's Apprentice (Dukas) 156
Soundararajan, Kannan 389
Space, nature of 130 195
Space, operators on 317—318
Sprague — Grundy theory 372
Sprague, Roland Percival 372
Square roots 41 43 176 178
Squaring function 37 42 201—202 206—209 240
St. Pafnuty of Borovsk 123
St. Petersburg Academy 30 57—58 122
St. Petersburg University 122
Stegun, Irene A. 373
Steiner, Jakob 119
Step functions 124 297—302
Stern, Moritz 27
Stevens, Wallace 198
Stieltjes integral 160
Stieltjes, Thomas 154 160 161 376
STIRLING, JAMES 123
Strachey, Lytton 370 380
Summation sign ( ) 78
Sylvester, James Joseph 154 225
te Riele, Herman 161 236 258
Teichmueller Theory 383
Teichmueller, Oswald 255—256 383
Telegraph, electric 120
Tenenbaum, Gerald 389
Theory of Numbers (Hardy and Wright) 302
Theory of performances 52
Theory of the Riemann Zeta-function, The (Titchmarsh) 217 384
Thread, The (Davis) 122
Three-body problem 314
Time reversal symmetry 316
Titchmarsh, Edward Charles 217 258 262 394
topology 18 121 209 374
Trace formula 321 388
Transcendental numbers 174 185 354
Trigonometry 18
Trinity College, Cambridge 193 223—224 225—226 229 287 379 380
Trinity Hall, Cambridge 380
Truman, Harry S. 166
Turan, Paul 238 239 378
Turing machine 261 391
Turing Prize 261
Turing Test 261
Turing, Alan 258 261—262 357 377 391 pl.
Twiddle principle 46
Twiddle sign 45 368
Uncle Petros and Goldbach's Conjecture (Doxiadis) 90
Universal Computer, The (Davis) 187
Universities, academies distinguished from 30
University of Bordeaux 158—159
University of Breslau 93 94
University of Bristol, England 390
University of Cambridge 259
University of Copenhagen 228
University of Leipzig 270
University of Louvain 161
University of Manchester 259
University of Marburg 270
University of Minnesota 322 357
University of Wales, Cardiff 391
University of Washington in Seattle 352
Upper bound 235—236
Value plane 219—221 335
van de Lune, Jan 257—258
Victoria, Queen of England 26
Vienna Academy 153
Vis viva equation 313 315
Volterra, Vito 92
von Beneckendorf und von Hindenburg, Paul 254
von Humboldt, Alexander 24 93
von Humboldt, Wilhelm 24 29 92
von Koch, Helge 237 240 242 244—245 381 397
von Lindemann, Ferdinand 174 185
von Mangoldt, Hans x 153 155 156 160—161 189 192 232
von Neumann, John 164 378 391
Vorhauer, Ulrike 350 390
w plane 379
Wagon, Stan 389
Wallace, William 92
Wave functions 318
Weber, Heinrich 29 119 257 366
Weber, Wilhelm 27 120 127 374
Wedeniwski, Sebastian 258 259
Weierstrass, Karl 135 164
Weil Conjectures 270 355
Weil, Andre 270 325 385 395 pl.
Wendland 22 94
Weyl, Hermann 170 255 385
Whitehead, Alfred North 225
Whitemore, Hugh 262
Wigner, Eugene 282 387
Wild Numbers, The (Schogt) 161
Wiles, Andrew 90 161 245 271 354—355
Wilhelm I, German Kaiser 160
William IV, King of England and Hanover 26
Wolfram, Stephen 389
Wright, Sir Edward 302
Yorke, James 387
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