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

Vinogradov      18
Vinogradov’s theorem      62
Volchkov      52
von Mangoldt      15 31 140 223 239 240 243 274 275 299 471
von Mangoldt’s function      125 464 471
von Mangoldt’s theorem      274 275
Waveform, Maass      101 106
Waveform, primitive      101
Weber      233
Weber series      233
Weber’s formula      233
Wedeniwski      126
Weierstrass      457
Weierstrass M-test      457
Weil      103—106 111 131 132 333 335
Weil conjecture      109 115 333
Weil — Guinand — Riemann formula      116
Weil’s explicit formula      104 128 129
Weil’s explicit formula, $\zeta(s)$       104
Weil’s explicit formula, L-function, number field      104
Weil’s explicit formula, zeta function, curve      104
Weil’s positivity criterion      128
Weinberger      441
Weyl      126 345 359
Weyl sum      126
Weyl’s inequality      359
Wiener      455 459 462 491
Wiener theory      462
Wiener theory, prime number theorem      462
Wiener’s Tauberian theorem      491
Wiener’s Tauberian theory      462
Wiles      4 101 126 130 135
Wilkins      193 201
Wilson      319
Wilson’s Theorem      319
winter      102
Winther      374
Wirsing      477
Wirsing’s mean value theorem      477
Xi function      51 313
Xian-Jin Li      128
Yau      333
Zagier      134
Zero, $(1 - 2^{1-2s})\zeta(2s)$       314
Zero, $(1 - 2^{1-2s})\zeta(2s)$ , location      314
Zero, $H(\lambda, z)$       51
Zero, $H(\lambda, z)$ , real      51
Zero,       352
Zero, , location      352
Zero, $L(s, \chi)$ , line $\mathfrak{R}(s) = 1$       373
Zero, $L(s, \chi)$ , location      373
Zero, $L(s, \chi_3)$       129 130
Zero, $L(s, \chi_k)$       132 133
Zero, $L(s, \chi_k)$ , connection      133
Zero, $L(s, \pi)$ , line $\mathfrak{R}(s) = 1$       114
Zero,       130
Zero,       222
Zero, , conjugate      222
Zero, , distribution      222 223
Zero, , location      222
Zero, $M_{Z, f}(t)$       152 155 162 164
Zero, $M_{Z, f}(t)$ , $\gamma$       155 164
Zero, $M_{Z, f}(t)$ , distribution      152 155 162
Zero, $M_{Z, f}(t)$ , location      152
Zero, $M_{Z, f}(t)$ , multiplicity      152
Zero, , asymptotic behavior      372
Zero,       344 345 349
Zero, , condensation point      345 349
Zero, , location      345 358
Zero,       348 349 370 372
Zero, , asymptotic behavior      348 370
Zero, , condensation point      348 349 370
Zero, , location      366 372
Zero, $\dfrac1{\zeta(s)}$       299 302
Zero, $\eta(s)$       49 56
Zero, $\eta(s)$ , critical line      49
Zero, $\eta(s)$ , critical strip      49
Zero, $\Lambda(s)$       111
Zero, $\Lambda(s)$ , location      111
Zero, $\Lambda(s, \chi)$       116
Zero, $\Lambda(s, \chi)$ , critical line      116
Zero, $\Lambda(s, \chi)$ , eigenvalue      116
Zero, $\Lambda(s, \chi)$ , location      116
Zero, $\Lambda(s,\pi)$       113 115
Zero, $\Lambda(s,\pi)$ , fluctuation      115
Zero, $\Lambda(s,\pi)$ , location      113 115
Zero, $\sin\theta(t)$       33
Zero, $\xi'(s)$       126 127
Zero, $\xi(s)$       15 19 27 31 38 97
Zero, $\xi(s)$ , argument principle      20
Zero, $\xi(s)$ , critical strip      19
Zero, $\xi(s)$ , distribution      97
Zero, $\xi(s)$ , imaginary part      38
Zero, $\xi(s)$ , location      38
Zero, $\Xi(t)$       127
Zero, $\xi(t)$ , distribution      204
Zero, $\xi(t)$ , location      204
Zero, $\xi(t)$ , multiplicity      101
Zero, $\xi(t)$ , multiplicity odd      101
Zero, $\xi(\hat{t})$       38
Zero, $\xi(\hat{t})$ , multiplicity      38
Zero, $\xi(\hat{t})$ , odd      38
Zero, $\zeta(s)$       211 213 214 227 240 242 243 311 313
Zero, $\zeta(s)$ , $\rho$       97 405 407
Zero, $\zeta(s)$ , $\rho_n$       429 431
Zero, $\zeta(s)$ , behavior      117 141 224 437 440 442
Zero, $\zeta(s)$ , computation      32
Zero, $\zeta(s)$ , conjugate      125 222 241 244 261 343
Zero, $\zeta(s)$ , conjugees      243 244
Zero, $\zeta(s)$ , connection      133
Zero, $\zeta(s)$ , counting      18
Zero, $\zeta(s)$ , critical line      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
Zero, $\zeta(s)$ , critical strip      18 19 24 30 41 313 322 407 462
Zero, $\zeta(s)$ , distribution      211 213
Zero, $\zeta(s)$ , eigenvalue      127 129 131
Zero, $\zeta(s)$ , imaginaires      241 242 247 254
Zero, $\zeta(s)$ , imaginary part      40 41 141 405 407 416 417 429 431 432 437 439 440 485 488 495
Zero, $\zeta(s)$ , integer part      130
Zero, $\zeta(s)$ , k-tuple correlation      442
Zero, $\zeta(s)$ , line $\mathfrak{R}(s) = 1$       16—18 61 114 125 211 214—216 234 235 238 240 322 323 455 461 464
Zero, $\zeta(s)$ , linear dependence      431
Zero, $\zeta(s)$ , linear operator      437 442
Zero, $\zeta(s)$ , location      14 15 24 30 70 97 101 102 116 125 126 139 140 202 211 213 242 254 258 274 311 313 322 342 343 403 405—407 409 429 432 434 435 445

Zero, $\zeta(s)$ , multiplicity      39 102 128 134 141 142 431 440—442 449
Zero, $\zeta(s)$ , pair correlation      485 487 498
Zero, $\zeta(s)$ , prime number      443
Zero, $\zeta(s)$ , relation between $\sigma$ and t      126 254 258 264 265 271—273 303 308 309
Zero, $\zeta(s)$ , simple      14 38 39 102 141 142 440
Zero, $\zeta(s)$ , symmetric      15 125
Zero, $\zeta(\frac12 + it)$       127
Zero, $\zeta_K(s)$       58 441
Zero, $\zeta_K(s)$ , critical line      441
Zero, $\zeta_K(s)$ , critical strip      441
Zero, alternating zeta function      348
Zero, alternating zeta function,       348 349 366 370 372
Zero, alternating zeta function, line $\mathfrak{R}(s) = 1$       348 373
Zero, Artin L-function      102
Zero, Bessel function      135
Zero, convolution function      142
Zero, Davenport — Heilbronn zeta function      144
Zero, Davenport — Heilbronn zeta function, asymptotic behavior      144
Zero, Davenport — Heilbronn zeta function, behavior      144
Zero, Davenport — Heilbronn zeta function, critical line      144
Zero, Davenport — Heilbronn zeta function, critical strip      144
Zero, Davenport — Heilbronn zeta function, distribution      144
Zero, Davenport — Heilbronn zeta function, location      144
Zero, Dirichlet L-function      102
Zero, Dirichlet series      351
Zero, elliptic curve L-function      135
Zero, elliptic curve L-function, multiplicity      135
Zero, Epstein zeta function      144
Zero, Epstein zeta function, critical strip      144
Zero, family      115
Zero, family, L-functions      115
Zero, L-function      100 102 105 116 132 133 135
Zero, L-function, critical line      60 132 135
Zero, L-function, critical strip      132
Zero, L-function, distribution      115 116 132
Zero, L-function, elliptic curve      135
Zero, L-function, fluctuation      115
Zero, L-function, high multiplicity      134 135
Zero, L-function, location      100
Zero, L-function, multiplicity      134
Zero, L-function, triple      134
Zero, Landau — Siegel      133 134
Zero, Maass L-function      102
Zero, meromorphic function      19
Zero, meromorphic function, counting      19
Zero, partial sum      71 339 350 351
Zero, partial sum, behavior      345
Zero, partial sum, condensation point      350 351 375
Zero, partial sum, Dirichlet series      351
Zero, partial sum, location      71 339
Zero, partial sum, Riemann zeta function      71
Zero, Riesz mean      372
Zero, Riesz mean, behavior      372
Zero, Riesz mean, condensation point      372
Zero, Z(t)      141—143 150—152 154 157 162
Zero, Z(t), $\gamma_n$       143 150
Zero, Z(t), distribution      151 152 154
Zero, Z(t), location      152
Zero, Z(t), multiplicity      141 151 152
Zero, Z(t), simple      141
Zero, Z(t, C)      103
Zero, zeta function      115 131
Zero, zeta function, critical line      115
Zero, zeta function, distribution      131
Zero, zeta function, eigenvalue      115
Zero, zeta functions      103 105
Zero-density theorem      66 114 115
Zero-free region      16
Zero-free region, $(z - 1)\zeta(s)$       455
Zero-free region,       347
Zero-free region,       352
Zero-free region, $L(s, \chi)$       373
Zero-free region, $L(s, \pi)$       114
Zero-free region,       343—346 361
Zero-free region,       348
Zero-free region, $\pi(x) - Li(x)$       403
Zero-free region, $\xi(t)$       204
Zero-free region, $\zeta'(s)$       50
Zero-free region, $\zeta(s)$       15 16 18 114 124 125 211 213 216 235 342—344 455 464
Zero-free region, Dirichlet series      223
Zero-free region, L-functions      116
Zero-free region, partial sum      71 339
Zero-free region, Riemann zeta function      71
Zeta functions      35 103 129 130 140 144 “Davenport “Epstein “Selberg
Zeta functions, $(1 - 2^{1-2s})\zeta(2s)$       314
Zeta functions, $(1 - 2^{1-2s})\zeta(s)$       348 (see also “Alternating zeta function”)
Zeta functions, $(z - 1)\zeta(s)$       455
Zeta functions, $\eta(s)$       35 36 56 “Dirichlet
Zeta functions, $\mathfrak{F}(\zeta(s))$       124
Zeta functions, $\mathfrak{R}(\zeta(s))$       124
Zeta functions, $\zeta(s)$       4 5 10—12 14 15 29 31 33 35 56 65 66 97 101 111 123 139 140 146 201 213 214 235 237 238 242 311 313 320 342 405 431 461
Zeta functions, $\zeta(s)$ , $L(s, \chi_1)$       56
Zeta functions, $\zeta(s)$ , $\zeta_K(s)$       58
Zeta functions, $\zeta(s)$ , behavior      34 66
Zeta functions, $\zeta(s)$ , critical line      34
Zeta functions, $\zeta(s)$ , derivative      49 101
Zeta functions, $\zeta(s)$ , integral formula      99
Zeta functions, $\zeta(s)$ , logarithm      16 99 204 213 214 322
Zeta functions, $\zeta(s)$ , logarithmic derivative      22 227 229 243 322 463 464
Zeta functions, $\zeta(s)$ , partial sum      343
Zeta functions, $\zeta(s)$ , peak      40
Zeta functions, $\zeta(s)$ , properties      322
Zeta functions, $\zeta(s)$ , s = 0      294
Zeta functions, $\zeta(s, a)$       144 (see also “Hurwitz zeta function”)
Zeta functions, $\zeta(s, C)$       103
Zeta functions, $\zeta(\sigma)$       17
Zeta functions, $\zeta^k(s)$       148
Zeta functions, $\zeta_K(s)$       58 336 337 441
Zeta functions, $\zeta_K(s)$ , numerator      336
Zeta functions, cohomology      105
Zeta functions, curve      103 (see also “Zeta functions C)$"/>”)
Zeta functions, Dirichlet      111 (see also “L-functions”)
Zeta functions, f(s)      see also “Davenport — Heilbronn zeta function”
Zeta functions, field      105
Zeta functions, finite field      131 132
Zeta functions, history      97
Zeta functions, number field      130
Zeta functions, variety      105
Zeta functions, Z(s)      145 (see also “Selberg zeta function”)
Zeta functions, Z(t, C)      103
Zeta functions, Z(t, C), degree      103
Zeta functions, Z(t, C), numerator      103
Zeta functions, Z(t, C), rational function      103
Zinoviev      62

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