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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
Class number formula      133
Class number problem      130 133
Class number, L-functions      133
Class number, lower bound      134
Class of functions      71
Class of functions, $E^{\beta}_{\alpha}$      151
Class of functions, $S^{\beta}_{\alpha}$      151
Class of functions, $T^{\beta}_{\alpha}$      162
Class of functions, convolution function      151
Class of functions, L-functions      see “L-functions”
Clay Mathematics Institute      4 93 95 109 111
Clay Mathematics Institute, prize      139
Closed orbit      52
Clustering point      see “Condensation point”
Co-NP      see “Complexity class”
Cohomology      103 105
Cohomology group      115
Cohomology group, Frobenius endomorphism      115
Cohomology, algebraic variety      103
Cohomology, zeta functions      105
Coincidence number      335
Compact support      54
Complex integration theory      462
Complex zero      see “Nontrivial zero”
Complexity class      511
Complexity class, co-NP      512 514
Complexity class, NP      512 514
Complexity class, P      509 511 514
Complexity theory      511
Composite integer      511
Computation, $A^*_T(u)$      429 433 435
Computation, $N_1(T)$      38
Computation, $\gamma_n$      432
Computation, $\gamma_n$, table      434 435
Computation, $\pi(x)$      46
Computation, $\pi(x)$, Gauss      46
Computation, $\rho_n$      101 141 429
Computation, $\zeta'(\rho_n)$      432
Computation, $\zeta(s)$      29 33 36 429 432
Computation, $\zeta(s)$, table      432
Computation, L(n)      374
Computation, N(T)      34
Computation, S(T)      150
Computation, Z(t)      32 33
Computation, zero, $\zeta'(s)$      38
Computation, zero, $\zeta(s)$      31 32 35 38 39 70 131
Computation, zero, Artin L-function      102
Computation, zero, Dirichlet L-function      102
Computation, zero, elliptic curve L-function      102
Computation, zero, Maass L-function      102
Comrie      417
Condensation point      345 349—351 375
Conductor      113 114
Conductor, curve      130
Conductor, elliptic curve      114
Conductor, representation      113
Congruence test      114
Conjectures, $F(X, T) \sim \dfrac{T}{2\pi}\log(T)$      485 488
Conjectures, $I_k(T) \sim c_k(\logT)^{k^2}$      67
Conjectures, $I_k(T) \sim \dfrac{a(k)g(k)}{\Gamma(k^2+1)}(\logT)^{k^2}$      67
Conjectures, $\pi(x) < Li (x)$      43 142 209
Conjectures, $\pi(x) < Li (x)$, disproof      43 44 405
Conjectures, $\pi(x) < Li (x)$, false      142
Conjectures, $\pi(x) < Li (x)$, Skewes      44
Conjectures, $\pi(x)\sim \int\limit_2^x\dfrac{dt}{\log (t)}$      124 125
Conjectures, Artin’s primitive root      64 114 520
Conjectures, Artin’s primitive root, conditional proof      64
Conjectures, Artin’s primitive root, consequence      520
Conjectures, Artin’s primitive root, generalized Riemann hypothesis      64 520
Conjectures, Artin’s primitive root, proof      64
Conjectures, Bieberbach      71
Conjectures, Bieberbach, de Branges      71
Conjectures, Bieberbach, proof      71
Conjectures, Birch and Swinnerton-Dyer      134 135
Conjectures, density of prime numbers      512
Conjectures, Gauss      124 125
Conjectures, Gauss, proof      133
Conjectures, Gauss, restatement      125
Conjectures, Goldbach      62 319
Conjectures, Goldbach (strong)      62
Conjectures, Goldbach (weak)      62
Conjectures, Goldbach (weak), generalized Riemann hypothesis      62
Conjectures, Goldbach (weak), statement implying      62
Conjectures, GUE      131
Conjectures, Hilbert — Polya      37 40
Conjectures, Keating — Snaith      67 115 131 132
Conjectures, Langlands      59
Conjectures, Mertens      37 69 125 141 433 435
Conjectures, Mertens, conditional disproof      433
Conjectures, Mertens, disproof      69 125
Conjectures, moments of L-functions      132
Conjectures, Montgomery — Odlyzko law      42
Conjectures, Montgomery’s pair correlation      41 43 130 134 437 488
Conjectures, Montgomery’s pair correlation, equivalent statement      502
Conjectures, pair correlation      488
Conjectures, Polya      429 431
Conjectures, Polya, disproof      429 431—433
Conjectures, Polya, Riemann hypothesis      431 432
Conjectures, Polya, verification      429
Conjectures, Shimura — Taniyama — Weil      111
Conjectures, Sophie Germain prime density      512 520
Conjectures, Turan      433
Conjectures, Turan, conditional disproof      433
Conjectures, Weil      109 115 333
Conjugacy class      145
Conjugacy class, norm      145
Connes      116
Conrad      101
Conrey      27 67 71 102 117 121 123 131 133 139
Constant      see “Euler’s constant”
Constant, $B_n$      30 158
Constant, $d_k$      36
Constant, $g_n$      33 34
Constant, $H_n$      48
Constant, $R_{2v}$      30 31
Constant, $\gamma$      see “Euler’s constant”
Constant, $\Lambda$      51
Constant, $\Lambda$, lower bound      51
Constant, $\lambda(n)$, Riemann hypothesis      50
Constant, $\lambda(n)$, sign      50
Constant, $\lambda_n$      50 128
Constant, $\rho$      173
Constant, de Bruijn-Newman      51
Constant, G      406 409
Constant, twin prime      520
Constante d’Euler      244 471
Contour integral      38 154 155 202 204 218 219 226 228 230 232 323 421 453 455 466 467
Contour integral, classical      455
Contour integral, finite      453 455
Contour integral, infinite      455
Contragredient representation      59 113
Convergence      49
Convergence theorem, Ingham      455
Convexity bound      126
Convolution      471
Convolution functions      139 151 157 162
Convolution functions, $M_{Z, f}(t)$      142 151 154
Convolution functions, $M_{Z, f}^{(k)}(t)$      151
Convolution functions, class      151
Convolution, Dirichlet      471
Correspondence      335
Correspondence, algebraic curve      335
Correspondence, complementary      336
Correspondence, curve      103
Correspondence, degree      335 336
Correspondence, irreducible      335
Correspondence, module      336
Correspondence, product      336
Critical line      15 30 34 49 111 125 140 141 144—146 150 165 222 311 343 440 462
Critical line, $\eta(s)$      49
Critical line, $\Lambda(s, \chi)$      116
Critical line, $\zeta(s)$      5 15 18 24 27 30—32 34 35 38 40 102 116 125 126 131 140—142 165 225 254 258 311 313 325 431 440
Critical line, $\zeta_k(s)$      441
Critical line, Davenport — Heilbronn zeta function      144
Critical line, L-function      60 132 135
Critical line, large value      142
Critical line, mean value formula      145
Critical line, zeros      102 115 116 125 126 131 132 135 140—142 144 165 225 254 258 311 313 431 440 441
Critical line, zeta function      115
Critical strip      15 18 29 30 49 125 140 144 322 462
Critical strip, $\eta(s)$      49
Critical strip, $\xi(s)$      19
Critical strip, $\zeta(s)$      18 19 24 30 41 313 322 407 462
Critical strip, $\zeta_K(s)$      441
Critical strip, Davenport — Heilbronn zeta function      144
Critical strip, Epstein zeta function      144
Critical strip, L-function      132
Critical strip, values of $\mu(\sigma)$      150
Critical strip, zeros      132 144 313 322 407 441 462
Cryptography      61 509 511
Curve      103 115 336
Curve, $\mathfrak{F}(\zeta(s)) = 0$      124
Curve, $\mathfrak{R}(\zeta(s)) = 0$      124
Curve, algebraic      335
Curve, conductor      130
Curve, nonsingular      102
Curve, projective      102
Cusp form      112
Cusp form, pseudo      129
CYCLE      53
Cycle, graph      53
Cycle, graph, Riemann hypothesis      53
Cyclotomic polynomial      517
Cyclotomic polynomial, finite field      517
Cyclotomic polynomial, irreducible factor      517
Daboussi      469 471 475 477
Dani      52
Dani’s theorem      52
Davenport      144 501
Davenport — Heilbronn zeta function      139 142 144
de Branges      71 116
de Bruijn      51 127
de Bruijn-Newman constant      51
de Bruijn-Newman constant, Riemann hypothesis      51
De La Vallee Poussin      9 16 47 61 114 116 125 211 234 235 237 238 241 243 282 293 294 317 322 323 455 461
Dedekind      130
Dedekind zeta function      58 441
Dedekind zeta function, $\zeta(s)$      58
Degree      17 112
Degree, $\zeta_K(s)$      336
Degree, algebraic extension      336
Degree, correspondence      335 336
Degree, divisor      103
Degree, polynomial      514
Degree, Z(t, C)      103
Delange      471
Deligne      103 105 131 132 134 333
Deligne’s theorem      103
Density hypothesis      146
Deshouillers      62
Determinant, Redheffer matrix      52
Deuring      133
diamond      101
Difference, $N(T) - N_0(T)$      152 165
Difference, $N(\sigma, T + 1) - N(\sigma, T)$      65
Difference, $N_M(T) - N(T)$      165
Difference, $S(T) - S_M(T)$      156
Difference, $\Pi(x) - \pi(x)$      410
Difference, imaginary parts of zeros      437 439
Difference, imaginary parts of zeros, distribution      439
Difference,$\pi(x) - Li(x)$      43 142 209 298 403 405
Difference,$\pi(x) - Li(x)$, sign      43 142 209 403 405 410 415 418 426
Differential equation      134
Diophantine approximation      431
Dirac’s function      439 442
Dirichlet      111 193 201 217 219 220 223 233 239
Dirichlet character      64 100 111 130
Dirichlet character, $\chi$      111
Dirichlet character, $\chi_D$      64
Dirichlet character, nonprincipal      64
Dirichlet character, primitive      101
Dirichlet convolution      471
Dirichlet eta function      49 55 56 “Zeta
Dirichlet eta function, convergence      56
Dirichlet eta function, Riemann hypothesis      49
Dirichlet L-function      56 102
Dirichlet L-series      56 60 64
Dirichlet L-series, $L(l, \chi_D)$      64
Dirichlet L-series, $L(s, \chi_k)$      56
Dirichlet L-series, $L(s,\chi)$      373
Dirichlet L-series, bound      64
Dirichlet polynomial      127 339 341 447
Dirichlet polynomial, approximative      339 341
Dirichlet series      10 11 115 140 216 217 219 223 232 314 323 325 328 351 459 462
Dirichlet series, $(1 - 2^{1-2s})\zeta(2s)$      314
Dirichlet series, $(1 - 2^{1-2s})\zeta(2s)$, summability      314
Dirichlet series, $L(s, \chi)$      111
Dirichlet series, $L(s, \chi_3)$      129
Dirichlet series, $L(s, \chi_k)$      56
Dirichlet series, $L(s, \Delta)$      59 112
Dirichlet series, $L_p(s)$      57
Dirichlet series, $L_v(s)$      221
Dirichlet series, $L_v(s)$, conjugate      221
Dirichlet series, $L_v(s)$, identity with conjugate      222
Dirichlet series, $\dfrac1{\zeta(s)}$      49 125 133 140 299 300 325 327 330 457
Dirichlet series, $\dfrac1{\zeta(s)}$, convergence      49 299 302
Dirichlet series, $\dfrac1{\zeta(s)}$, derivative      299
Dirichlet series, $\dfrac{\zeta'(s)}{\zeta(s)}$      322 444 464
Dirichlet series, $\dfrac{\zeta(2s)}{\zeta(s)}$      431
Dirichlet series, $\eta(s)$      56 98 348
Dirichlet series, $\log(\zeta(s))$      322
Dirichlet series, $\psi(x)$      125
Dirichlet series, $\Sigma_n\dfrac{\mu(n)}{n}$      325 327 330
Dirichlet series, $\zeta(s)$      10 12 55 97 111 123 139 201 203 242 320 342 461
Dirichlet series, $\zeta(s)$, convergence      10 55 123 201
Dirichlet series, $\zeta(s)$, real line      10
Dirichlet series, coefficient      455
Dirichlet series, coefficient, $c_n$      27
Dirichlet series, general      216 217
Dirichlet series, L-function, primitive waveform      101
Dirichlet series, ordinary      217
Dirichlet series, Parseval’s identity      446
Dirichlet series, partial sum      351
Dirichlet series, summability      314
Dirichlet series, zero-free region      223
Dirichlet’s class number formula      133
Dirichlet’s Theorem      381 392 416 426 431
Dirichlet’s theorem, proof      392
Discrete measure      54
Discrete measure, Riemann hypothesis      54
Discrete spectrum      147
Discriminant      112 133
Distribution des nombres premiers      224
Distribution des zeros, $L_{\nu}(s)$      222 223
Distribution of prime numbers      63 97—100 115 124 127 140 224 225 231 233 235 237 239 242 317 319 320 379 477 478 489 509
Distribution of values, $\zeta(\frac12 + it)$      132
Distribution of zeros, $L_{\nu}(s)$      222 223
Distribution of zeros, $M_{Z, f}(t)$      152 155 162
Distribution of zeros, $\xi(t)$      204
Distribution of zeros, $\zeta(s)$      41 65 97 101 124 125 131 133 146 165 274 321 342 440 445 498
Distribution of zeros, $\zeta(s)$, approximation      440
Distribution of zeros, $\zeta(s)$, upper bound      445
Distribution of zeros, L-functions      115 116 132
Distribution of zeros, L-functions, upper bound      115
Distribution of zeros, Z(t)      151 152 154
Distribution of zeros, zeta function      131
Distribution of zeros, zeta function, finite field      131
Divisor      48 103 335 336
Divisor function      47 48 148
Divisor group      102 103 105
1 2 3 4 5 6 7 8 9
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