Borwein P., Choi S., Rooney B. — The Riemann Hypothesis :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

Prime number, product      319 521
Prime number, product, lower bound      521
Prime number, property      511
Prime number, Riemann zeta function      46
Prime number, set      511
Prime number, Sophie Germain      512 520
Prime number, Sophie Germain, density      512 520
Prime number, spacing      489
Prime number, sum of three      62
Prime number, sum of two      62
Prime number, twin      41 130
Prime number, twin, constant      520
Prime number, twin, distribution      41 130
Prime number, zeros of $\zeta(s)$       443
Prime, divisor      104
Prime, representation      58
Primitive character      56
Primitive root      64
Primitive waveform      101
Primzahlsatz      319
Principal character      56
Principal value, $\pi(x)$       296
Principal value, Li(x)      240
Problems of the millennium      95 97 109 111 139
Product representation      see “Euler product”
Product representation, $L(s, \chi_3)$       130
Product representation, $L(s, \Delta)$       59 112
Product representation, $L(s, \pi)$       59
Product representation, $L(s, \pi_p)$       59
Product representation, $L(s, \pi_{\infty})$       59
Product representation,       130
Product representation, $L_{\Delta}(s)$       130
Product representation, $L_{\nu}(s)$       221
Product representation, $\dfrac1{\zeta(s)}$       125 299
Product representation, $\xi(s)$       15
Product representation, Hadamard      21
Product representation, Hadamard, logarithmic derivative      21
Progression arithmetique, formes quadratiques      233
Progression arithmetique, nombres premiers      233 241
Projective curve      102
Projective curve, nonsingular      102
Projective variety      105
Projective variety, nonsingular      105
Pseudo cusp form      129
Pseudo cusp form, eigenvalue      129
Purdue      71
Quadratic form      233 337
Quadratic form, arithmetic progression      233
Quadratic form, equivalence class      133
Quadratic form, negative semidefinite      105
Quadratic form, self-intersection      105
Quadratic form, ternary      114
Quadratic twist      132
Quantum chaos      114
Rabin      63 512
Rabin’s primality testing algorithm      512
Racine      see “Zero”
Rademacher      63 70 126
Rains      48
Ram Murty      64
Ramachandra      67 149 150
Ramanujan      114 311
Ramanujan property      100
Ramanujan’s tau function      130 (see also “Arithmetic functions
random matrix      40 42 109
Random matrix ensemble      115
Random matrix theory      40 42 121 130—132 134 135 139
Random matrix theory, Hilbert      40
Random matrix theory, Polya      40
Random matrix theory, Riemann hypothesis      40
Random matrix, Riemann hypothesis      40
Random walk      6 7
Rational function      35 336
Rational function, Z(t, C)      103
Rational point      134 135
Rational point, elliptic curve      135
Reciprocity law      512
Reciprocity law, primality test      512
Redheffer      53 129
Redheffer matrix      52
Redheffer matrix, determinant      52
Redheffer matrix, Riemann hypothesis      53
Relation, $\pi(x)$ and $\psi(x)$       465
Relation, $\sigma$ and t      126 254 258 264 265 303 308 309
Renyi      483
Representation      58 112
Representation, $\pi$       58 59 112
Representation, $\pi_p$       58 112
Representation, $\pi_v$       58 112
Representation, $\pi_{\infty}$       58 112
Representation, automorphic      100
Representation, automorphic cuspidal      58 112
Representation, conductor      113
Representation, contragredient      59 113
Representation, irreducible unitary      58 112
Representation, local      58 112
Representation, prime      58
Residue      38 99
Residue theorem      38 154 155 161 456
Residue, integer modulo n      517
Residue, introspective integer modulo n      517
Residue, pole      38
Residue, pole, $\dfrac{\zeta'(s)}{\zeta(s)}$       243 244
Residue, pole, $\xi_k(s)$       218
Residue, pole, $\zeta(s)$       15
Residue, pole, $\zeta(\sigma)$       17
Residue, polynomial      517
Rh      see “Riemann hypothesis”
Ribet      111
Richert      497
Riemann      3 4 9 10 12 14 15 19 31 32 38 39 43 70 97 99 100 111 123—125 140 141 169 193 201 213 224 240 313 317 321 322 467
Riemann hypothesis      3—6 15 29 37 55 61 70 93 95 97 99 101 109 111 121 123 125 126 137 139—141 162 165 169 193 311 322 325 342 405 429 462 “Generalized “Grand
Riemann hypothesis, $L(s, \chi_3)$       130
Riemann hypothesis, $L(s, \chi_k)$ , implication      133
Riemann hypothesis, $L(s, \chi_k)$ , verification      132
Riemann hypothesis,       130
Riemann hypothesis, $L_{\Delta}(s)$       130
Riemann hypothesis, $\dfrac{\xi'(s)}{\xi(s)}$       50
Riemann hypothesis, $\eta(s)$       56
Riemann hypothesis, $\Lambda(s)$       111
Riemann hypothesis, $\Lambda(s, \pi)$       117
Riemann hypothesis, $\lambda_N$       50
Riemann hypothesis, $\zeta(s, C)$       103
Riemann hypothesis, $\zeta_K(s)$       58 333 337
Riemann hypothesis, $\zeta_K(s)$ , consequence      337
Riemann hypothesis, $\zeta_K(s)$ , proof      333 337
Riemann hypothesis, algorithm      29
Riemann hypothesis, axioms      130
Riemann hypothesis, Bertrand’s postulate      63
Riemann hypothesis, conditional disproof      137 139 149 165
Riemann hypothesis, connection      145 351
Riemann hypothesis, connection, Lindelof hypothesis      145
Riemann hypothesis, consequence      41 43 44 61 63 65—67 345 358 405 429 431 432 437 439—441 485 487—490 497
Riemann hypothesis, consequence, Titchmarsh      65
Riemann hypothesis, convolution function      139 162
Riemann hypothesis, curve      115
Riemann hypothesis, curve, proof      131
Riemann hypothesis, cycle, graph      53
Riemann hypothesis, Davenport — Heilbronn zeta function, false      144
Riemann hypothesis, de Bruijn — Newman constant      51
Riemann hypothesis, Dirichlet eta function      49
Riemann hypothesis, Dirichlet L-function      101 102
Riemann hypothesis, discrete measure      54
Riemann hypothesis, disproof      93 162 165
Riemann hypothesis, disproof, false      70
Riemann hypothesis, disproof, Rademacher      70
Riemann hypothesis, doubts      93 137 139 142 145 162 165
Riemann hypothesis, Epstein zeta function, false      144
Riemann hypothesis, equivalent statement      6 18 45—54 56 70 100 102 105 116 125 127—129 140 141 152
Riemann hypothesis, equivalent statement, analytical      49

Riemann hypothesis, equivalent statement, number theoretic      45
Riemann hypothesis, ergodic theory      52
Riemann hypothesis, Euler’s constant      52
Riemann hypothesis, evidence      18 32 37 39 101 104 116 126 142
Riemann hypothesis, extension      61 95 97
Riemann hypothesis, Farey series      49
Riemann hypothesis, finite field      335
Riemann hypothesis, finite field, proof      335
Riemann hypothesis, function (finite field), proof      335
Riemann hypothesis, function field      333 335
Riemann hypothesis, function field, proof      333
Riemann hypothesis, function field, Weil      333 335
Riemann hypothesis, generalization      111
Riemann hypothesis, Hardy and Littlewood      51
Riemann hypothesis, Hardy’s theorem      24 27
Riemann hypothesis, Hilbert — Schmidt integral operator      52
Riemann hypothesis, history      39
Riemann hypothesis, hypothesis H      44
Riemann hypothesis, implication      126 128 141 143 145 148 150 151 162 163 165
Riemann hypothesis, implication, Lindelof hypothesis      146
Riemann hypothesis, intuitive statement      6
Riemann hypothesis, L-functions      101 106 130
Riemann hypothesis, L-functions, consequence      100
Riemann hypothesis, L-functions, global      100
Riemann hypothesis, L-functions, Maass waveform      102
Riemann hypothesis, L-functions, modular form      102
Riemann hypothesis, L-functions, primitive waveform      101
Riemann hypothesis, L-functions, verification      102
Riemann hypothesis, Lindelof hypothesis      65
Riemann hypothesis, Lindelof’s relaxation      65
Riemann hypothesis, Liouville’s function      6 46
Riemann hypothesis, Mertens’ conjecture      69
Riemann hypothesis, Mertens’ function      47
Riemann hypothesis, Montgomery’s pair correlation, conjecture      41
Riemann hypothesis, necessary condition      24 27
Riemann hypothesis, Nyman — Beurling equivalent form      53
Riemann hypothesis, order, symmetric group element      54
Riemann hypothesis, original statement      193 322
Riemann hypothesis, partial sum      71 339 343 344 347 348
Riemann hypothesis, Polya’s conjecture      429 431 432
Riemann hypothesis, prime number theorem      43
Riemann hypothesis, probabilistic argument      127
Riemann hypothesis, proof      72
Riemann hypothesis, proof, false      69 72
Riemann hypothesis, proof, ideas      93
Riemann hypothesis, quasi      134
Riemann hypothesis, random matrix      40 42
Riemann hypothesis, random matrix theory      40
Riemann hypothesis, Redheffer matrix      53
Riemann hypothesis, Salem      52
Riemann hypothesis, Skewes number, bound      43
Riemann hypothesis, statement affecting      148
Riemann hypothesis, statement implying      57 70 71 141 146 157 162 254 258 339 343 344 347 348 364 373 374 431 490
Riemann hypothesis, sum of divisors function      48
Riemann hypothesis, variety (finite field)      105 115
Riemann hypothesis, variety (finite field), proof      105
Riemann hypothesis, variety (general), proof      131
Riemann hypothesis, verification      19 24 27 29 32 34 35 37—39 42 101 102 116 126 127 131 137 141 142 255 258 311 374 429 440
Riemann hypothesis, Z(s)      145
Riemann hypothesis, Z(s), true      145
Riemann hypothesis, Z(t, C)      103
Riemann hypothesis, zeta function, number field      58 130
Riemann hypothesis, zeta functions      103
Riemann hypothesis, zeta functions, proof      103
Riemann summability      490 491 495
Riemann surface      101 193
Riemann zeta function      4 5 9—12 14 15 29 31 33 35 37 95 97 111 121 123 129 139 169 193 201 211 213 235 237 238 242 311 313 320 339 341 342 403 405 429 431 439 459 461 488
Riemann zeta function, behavior      69
Riemann zeta function, integral formula      464
Riemann zeta function, L-functions      100
Riemann zeta function, partial sum      71 339 343
Riemann zeta function, prime numbers      46
Riemann zeta function, properties      193 459 464
Riemann — Lebesgue lemma      467
Riemann — Roch theorem      103 105
Riemann — Siegel formula      32—34 38 39 101 126 141 152 158 161
Riemann — Siegel formula, Euler — MacLaurin summation formula      32
Riemann — Stieltjes assertation      224
Riemann — von Mangoldt formula      140 144
Riemann’s explicit formula      104 125
Riemann’s formula      99 313
Riemann’s memoir      15 99 140 193 195—200 321
Riemann’s memoir, English translation      193 201
Riesz      314
Riesz mean      347 349
Riesz’s theorem      314
Ring,       514
Ring, $\mathbb{A}$       58 112
Ring, $\mathbb{R}*$       54
Ring, $\mathbb{Z}/p\mathbb{Z}$       64
Ring, $\mathcal{O}_K$       58
Ring, $\mathcal{Z}$       514
Ring, adeles      58 112
Ring, integers      58 514
Ring, integers modulo n      514
Ring, polynomial      512
RMT      see “Random matrix theory”
Robin      48
Rogosinski      495
Rolle’s Theorem      126
Root      see “Zero”
Root, primitive      64
rosser      34
Rosser’s rule      34
Rosser’s rule, false      34
Rosser’s rule, false, Lehman      34
Rouche      371
Rouche’s Theorem      371
Rubinstein      132
Rudnick      105 134
Rumely      512
Running time      509 511—514
Ruzsa      484
Sabbagh      71
Saffari      487 504
Sahai      518
Saias      127
Salem      51 52
Salem, Riemann hypothesis      52
Sarnak      60 100 105 109 111 131 132 134
Saxena      63 114 509 511
Schaar      245
Schlomilch      217
Schlomilch function      217
Schmidt      52 103
Schneider      126
Schonhage      35 131
Schwarz      163 447 481 484 505
Selberg      27 61 102 126 128 130 131 150 152 373 377 379 391 392 396 398 399 440 455 461 469 471 472 475 477 478 485 487 496 498 500
Selberg zeta function      145 (see also “Zeta functions Z(s)”)
Selberg, Dirichlet’s theorem      392
Selberg’s asymptotic formula      377 379 383 389 391 469 471 475 477—479
Selberg’s asymptotic formula, proof      383 392
Selberg’s result      144
Selberg’s result, extension      485
Selberg’s trace formula      128 129
Selberg’s upper bound sieve      478
Semi-simple group      116
Series representation      see “Dirichlet series” “Partial
Series representation, $F(y, \lambda)$       423
Series representation,       130
Series representation, $L_{\Delta}(s)$       130
Series representation, $\dfrac{\xi'(s)}{\xi(s)}$       143
Series representation, $\dfrac{\zeta'(s)}{\zeta(s)}$       23 227 229 259 300 322
Series representation, $\dfrac{\zeta'(s)}{\zeta^2(s)}$       299
Series representation, $\log((s - 1)\zeta(s))$       98
Series representation, $\log(\xi(s))$       204
Series representation, $\log(\zeta(s))$       16 204 213 216
Series representation, $\log(\zeta(s))$ , convergence      213
Series representation, $\mathbb{R}(\log(\zeta(s)))$       214

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