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Borwein P., Choi S., Rooney B. — The Riemann Hypothesis
Borwein P., Choi S., Rooney B. — The Riemann Hypothesis



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Название: The Riemann Hypothesis

Авторы: Borwein P., Choi S., Rooney B.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 576

Добавлена в каталог: 04.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Nontrivial zero, $L(s, \chi_3)$      130
Nontrivial zero, $L(s, \chi_k)$      57
Nontrivial zero, $L_v(s)$      222
Nontrivial zero, $L_{\Delta}(s)$      130
Nontrivial zero, $\eta(s)$      49
Nontrivial zero, $\xi(\frac12 + it)$      127
Nontrivial zero, $\zeta(s)$      5 15 18 38—41 70 97 99 125 139—143 165 242—244 247 274 311 313 321 322 342 349 403 405 429 431 437 439 462 485 488 495
Nontrivial zero, $\zeta(s)$, $\lim\inf(1 - \sigma_n)$      241 261 265 270
Nontrivial zero, $\zeta(s)$, $\lim\sup(\sigma_n)$      241 258 261
Nontrivial zero, $\zeta(s)$, $\rho$      125 143 242
Nontrivial zero, $\zeta(s)$, $\rho_n$      429 431
Nontrivial zero, $\zeta(s)$, argument principle      19
Nontrivial zero, $\zeta(s)$, conjugate      243
Nontrivial zero, $\zeta(s)$, counting      18 19
Nontrivial zero, $\zeta(s)$, distribution      440
Nontrivial zero, $\zeta(s)$, existence      27 38 42 322 440
Nontrivial zero, $\zeta(s)$, proportion      27
Nontrivial zero, $\zeta(s)$, simple      102
Nontrivial zero, $\zeta(s)$, smallest      35 38 41 70 101 102 139 243 405 416 417 429 431 432
Nontrivial zero, $\zeta(s)$, symmetric      15
Nontrivial zero, $\zeta_K(s)$      58
Nontrivial zero, $|Lambda(s)$      111
Nontrivial zero, Davenport — Heilbronn zeta function      144
Norm, conjugacy class      145
Norm, divisor      103
Norm, integral ideal      58
NP      see “Complexity class”
Number field      58
Number of primes      97 193 201 209
Numerator, $\zeta_K(s)$      336
Numerator, $\zeta_K(s)$, degree      336
Numerator, $\zeta_K(s)$, polynomial      336
Numerator, Z(t, C)      103
Nyman      53 127
Nyman — Beurling equivalent form      53
Nyman — Beurling equivalent form, Riemann hypothesis      53
Nyman — Beurling theorem      127
Odlyzko      35 42 51 69 70 102 105 115 116 125 126 131 141 142
Odlyzko — Schonhage algorithm      35
Operator      26
Operator, Hecke      101
Operator, hermitian      40 127
Operator, integral      52
Operator, integral, Hilbert — Schmidt      52
Operator, Laplace      128
Operator, linear      105 437 442
Operator, self-adjoint      115
Orbit      52
Orbit, closed      52
Order      see “Multiplicity”
Order, $(s - l)\zeat(s)$      145
Order, $E_1(T)$      145
Order, $E_2(T)$      145 147
Order, $E_k(T)$      148
Order, $E_m$      33
Order, $M_{Z,f}^{(k)}(t)$      152
Order, $N(T) - N_0(T)$      165
Order, $N(\alpha, T)$      102
Order, $N(\alpha, T)$, Ingham’s exponent      102
Order, $N_M(T) - N(T)$      165
Order, $S(T)S      66
Order, $S_1(T)$      66
Order, $theta(x)$      321
Order, $Z^{(k)}(t)$      151
Order, $\pi(x) - Li(x)$      241 298
Order, $\Pi(x) - \pi(x)$      410
Order, $\pi(x)$      320 321
Order, $\psi(x)$      323
Order, $\sigma(y)$      281 282
Order, $\Sigma_n\dfrac{\mu(n)}{n}$      302
Order, $\Sigma_{rho}\dfrac{y^{\sigma-1}}{t^2}$      277 278
Order, $\Sigma_{rho}\dfrac{y^{\sigma-1}}{\sigma^2+t^2}$      279—281
Order, $\vartheta(x)$      393
Order, $\xi(s)$      143
Order, $\zeta(s)$, bound      146
Order, $\zeta(s)$, critical line      146
Order, $\zeta(\frac12 + it)$      126 146
Order, group element      53
Order, integer modulo n      514
Order, Li(x)      409
Order, M(x)      69 70 125
Order, R(x)      386
Order, S(T)      125 140
Order, symmetric group element      53
Order, symmetric group element, equivalent statement      54
Order, Z(s)      145
Order, Z(t)      151
Orthogonal matrix      105 132
Orthogonal matrix, eigenvalue      105
Oscillations, of Z(t)      150 151
P      see “Complexity class”
Pair correlation      130 134 437 439 442 485 487 488
Pair correlation conjecture      488
Pair correlation function      42 437 442
Pair correlation function, eigenvalue, Gaussian unitary ensemble      42
Pair correlation function, eigenvalue, Hermitian matrix      437 442
Pair correlation function, eigenvalue, unitary matrix      437 442
Pair correlation function, plot      42
Pair correlation, eigenvalue      437
Pair correlation, eigenvalue, symmetric matrix      437 442
Pair correlation, eigenvalue, symplectic matrix      437 442
Pair correlation, Montgomery      502
Pair correlation, prime numbers      485 487 489
Pair correlation, short interval      485 487
Pair correlation, zeros of $\zeta(s)$      42 442 485 487 498
Parseval      446
Parseval’s identity      446
Partial sum      339 373
Partial sum, $L(s, \chi)$      373
Partial sum, $r_n(s)$      345
Partial sum, $U_n(s)$      343 347 349
Partial sum, $V_n(s)$      348 366
Partial sum, $W_n(s)$      353
Partial sum, alternating zeta function      348 (see also “Partial sum
Partial sum, Dirichlet series      351
Partial sum, power series      375
Partial sum, Riemann hypothesis      71 339 343 344 347 348
Partial sum, Riemann zeta function      71 339 343
Partial sum, zero      339 350 351
Partial sum, zero, behavior      345
Partial sum, zero, condensation point      350 351 375
Partial sum, zero-free region      339
Paths, $0 \searrow 1$      159
Paths, $0\swarrow1$      159
Peak      162
Peak, $\zeta(s)$      40
Peak, $\zeta(\frac12 + it)$      102
Peak, Z(t)      150 151
Perfect square      520
petersen      374
Phragmen — Lindelof theorem      126
Piltz      223
Plancherel      502
Plancherel’s identity      502
Poincare      224
Poisson summation      13
Pole, $L_1(s)$      221
Pole, $L_1(s)$, multiplicity      221
Pole, $L_1(s)$, simple      221
Pole, $L_v(s)$      221
Pole, $Z_2(\xi)$      147
Pole, $Z_2(\xi)$, critical line      147
Pole, $Z_2(\xi)$, multiplicity      147
Pole, $Z_2(\xi)$, multiplicity five      147
Pole, $Z_2(\xi)$, simple      147
Pole, $\dfrac{\zeta'(s)}{\zeta(s)}$, residue      243 244
Pole, $\Gamma(s)$      13 14 242
Pole, $\Gamma(s)$, residue      13
Pole, $\Gamma(s)$, simple      14
Pole, $\xi_k(s)$      218
Pole, $\xi_k(s)$, multiplicity      218
Pole, $\xi_k(s)$, residue      218
Pole, $\xi_k(s)$, simple      218
Pole, $\zeta(s)$      11 14 15 38 97 101 123 133 139 202 213 216 322 342
Pole, $\zeta(s)$, multiplicity      11 14
Pole, $\zeta(s)$, residue      11 15
Pole, $\zeta(s)$, simple      11 14 15 97 101 123 139 213 322 342
Pole, $\zeta(s, C)$      103
Pole, $\zeta(s, C)$, multiplicity      103
Pole, $\zeta(s, C)$, simple      103
Pole, $\zeta(\sigma)$      17
Pole, $\zeta(\sigma)$, residue      17
Pole, $\zeta(\sigma)$, simple      17
Pole, L-function      100
Pole, L-function, location      100
Pole, Li(s)      221
Pole, meromorphic function      19
Pole, meromorphic function, counting      19
Pole, residue      38
Pole, Z(t, C)      103
Pole, Z(t, C), multiplicity      103
Pole, Z(t, C), simple      103
Pole, zeta functions      103
Polya      37 40 105 115 127 130 135 311 356 358 374 431
Polya’s conjecture, Riemann hypothesis      429 431 432
Polya’s theorem      356 357
Polynomial $Q_n(X)$      517
Polynomial $\zeta_K(s)$      336
Polynomial Artin L-function      335
Polynomial Bernouilli      30
Polynomial characteristic      67 131
Polynomial Chebyshev      36
Polynomial cyclotomic      517
Polynomial degree      514
Polynomial introspective      516
Polynomial irreducible      514 517
Polynomial residue      517
Polynomial ring      512
Polynomial ring, Fermat’s little theorem      512
Polynomial ring, finite field      512
Polynomial time      509 511 512
Pomerance      512 521
Positive integer, introspective      516 517
Positive integer, perfect square      520
Poulsen      374
Power series      375
Power series, partial sum      375
Pratt      512
Premiers de la progression arithm?etique      241
Primality testing algorithms      63 319 509 511 513
Primality testing algorithms, Adleman — Huang      512
Primality testing algorithms, Adleman — Pomerance — Rumely      512
Primality testing algorithms, Atkin      512
Primality testing algorithms, conditional      512
Primality testing algorithms, elliptic curve      512
Primality testing algorithms, exponential time      512
Primality testing algorithms, exponential time, deterministic      512
Primality testing algorithms, extended Riemann hypothesis      509 512
Primality testing algorithms, Fermat’s little theorem      511
Primality testing algorithms, Fermat’s little theorem, polynomial ring      512
Primality testing algorithms, generalized Riemann hypothesis      63
Primality testing algorithms, Goldwasser — Kilian      512
Primality testing algorithms, Jacobi symbol      512
Primality testing algorithms, Miller      114 512
Primality testing algorithms, Miller — Rabin      63
Primality testing algorithms, Miller — Rabin, conditional deterministic      63
Primality testing algorithms, Miller — Rabin, conditional polynomial time      63
Primality testing algorithms, Miller — Rabin, generalized Riemann hypothesis      63
Primality testing algorithms, Miller, running time      114
Primality testing algorithms, polynomial time      509 511—513
Primality testing algorithms, polynomial time, deterministic      509 511 512
Primality testing algorithms, polynomial time, proof      509 513
Primality testing algorithms, polynomial time, randomized      512 513
Primality testing algorithms, Rabin      512
Primality testing algorithms, reciprocity law      512
Primality testing algorithms, running time      511 513
Primality testing algorithms, Solovay — Strassen      63
Primality testing algorithms, Solovay — Strassen, conditional deterministic      63
Primality testing algorithms, Solovay — Strassen, generalized Riemann hypothesis      63
Primality testing algorithms, Solovay’s primality test      512
Primality testing algorithms, Sophie Germain prime density      512 520
Primality testing algorithms, Sophie Germain prime density, time complexity      512 520
Primality testing algorithms, Strassen      512
Primality testing algorithms, unconditional      509 511 512
Primality testing problem      512
Prime      see “Prime number”
Prime counting function      46 193 201 209 241 292 461
Prime decomposition      319
Prime k-tuple hypothesis      490
Prime k-tuple hypothesis, weak      490
Prime number      63 64 317 319 509 511
Prime number theorem      7 43 46 61 113 125 171 182 211 235 298 317 319—321 325 327 328 377 379 389 391 392 453 455 459 461 469 471 509
Prime number theorem, arithmetic progression      381 392
Prime number theorem, arithmetic progression, proof      381 392
Prime number theorem, auxiliary Tauberian theorem      463
Prime number theorem, conditional proof      171 182
Prime number theorem, consequence      447
Prime number theorem, Dirichlet series      325
Prime number theorem, equivalent statement      8 321 323 325 328 379 386 392 453 455 457 463 465 475 477 479
Prime number theorem, exposition      317
Prime number theorem, Gauss      46
Prime number theorem, history      317 319 459 462
Prime number theorem, Ikehara — Wiener Tauberian theorem      459 462
Prime number theorem, intuitive statement      8
Prime number theorem, large sieve      475 477
Prime number theorem, large sieve inequality      475
Prime number theorem, Liouville’s function      7
Prime number theorem, proof      18 125 211 235 299 320 325 327 377 379 389 391 401 453 455 471
Prime number theorem, proof, analytic      8 453 455
Prime number theorem, proof, Daboussi      469 475 477
Prime number theorem, proof, de la Vallee Poussin      8 9 47 61 125 235 317 322 323 455 461
Prime number theorem, proof, elementary      8 61 377 379 389 391 398 469 475
Prime number theorem, proof, Erdos      61 377 389 391 455 461 469 477 479
Prime number theorem, proof, Erdos — Selberg      389 399 400
Prime number theorem, proof, Hadamard      8 47 61 125 211 235 317 322 323 455 461
Prime number theorem, proof, Hardy — Littlewood      325 327
Prime number theorem, proof, Hildebrand      475 477
Prime number theorem, proof, Ikehara      455
Prime number theorem, proof, Korevaar      8 61 459 463
Prime number theorem, proof, Newman      61 453 455 457 459 462
Prime number theorem, proof, Selberg      61 377 379 386 387 389 392 396 455 461 469 477
Prime number theorem, proof, simplification      389 392 398 399
Prime number theorem, proof, Wiener      455
Prime number theorem, Riemann hypothesis      43
Prime number theorem, similar theorem      325 327
Prime number theorem, Wiener theory      462
Prime number, accumulation      201
Prime number, arithmetic progression      63 111 133 233 241 497
Prime number, arithmetic progression, distribution bound      115
Prime number, arithmetic progression, upper bound      497
Prime number, asymptotic behavior      225 231 233 235 239 240 274 317 319 461 489 520
Prime number, bad      394
Prime number, cardinality      319 320
Prime number, decomposition      319
Prime number, density      209 520
Prime number, density, sieve      512
Prime number, distribution      18 63 97—100 115 124 127 140 224 225 231 233 235 237 239 242 317 319 320 379 477 478 489 509
Prime number, distribution, sieve      477
Prime number, distribution, upper bound      477 478
Prime number, estimate      477
Prime number, good      394 398
Prime number, good, existence      394 396 399
Prime number, interval      63
Prime number, large      511
Prime number, location      63 379
Prime number, pair      41 130 319
Prime number, pair correlation      485 487 489
Prime number, pair, distribution      41 130
Prime number, power      500
Prime number, power, location      500
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