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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
Divisor problem      66 149
Divisor problem, ternary additive      149
Divisor, degree      103
Divisor, effective      103
Divisor, norm      103
Divisor, positive      103
Divisor, prime      104
Doetsch      462
Duality, prime numbers and zeros      128
Dyson      40 42 102 130 437 442
Edwards      97 144 462
Effinger      62
Eigenfunction      101
Eigenvalue, Frobenius endomorphism      103 115
Eigenvalue, Gaussian unitary ensemble      42
Eigenvalue, Gaussian unitary ensemble, normalized      42
Eigenvalue, Hecke operator      101
Eigenvalue, Hermitian matrix      130 131 437 442
Eigenvalue, Hermitian operator      40 127
Eigenvalue, Laplace operator      128
Eigenvalue, linear operator      437 442
Eigenvalue, linear operator, self-adjoint      105
Eigenvalue, linear operator, zeros of $\zeta(s)$      437 442
Eigenvalue, linear transformation      115
Eigenvalue, matrix      40
Eigenvalue, matrix, distribution      105 115
Eigenvalue, orthogonal matrix      105
Eigenvalue, pair correlation      437
Eigenvalue, pair correlation function      437 442
Eigenvalue, pseudo cusp form      129
Eigenvalue, spacing, Gaussian unitary ensemble      42
Eigenvalue, symmetric matrix      437 442
Eigenvalue, symplectic matrix      105 437 442
Eigenvalue, unitary matrix      105 129 437 442
Eigenvalue, zeros, $\Lambda(s, \chi)$      116
Eigenvalue, zeros, $\zeta(s)$      40 41 127 129 131
Eigenvalue, zeros, zeta function      115
Eilertsen      374
Einstein      70
Einstein’s relativity theory      70
Eisenstein      116 193
Eisenstein series      116
Eisenstein series, inner product formula      116
Elliott      478 483
Elliptic curve      100 102 114 130 134 135 512
Elliptic curve, conductor      114
Elliptic curve, isogenous      114
Elliptic curve, L-function      100
Elliptic curve, modularity      100
Elliptic curve, primality test      512
Elliptic curve, rational point      135
Elliptic curve, reduction modulo p      114
Elliptic function      314
Embedding projective      105
Enestrom — Kakeya theorem      351
Enke      46
Epstein zeta function      144
Equidistribution rate      114
Equivalence class      133
Equivalent extended Riemann hypothesis      57
Equivalent form      53
Equivalent form, Nyman — Beurling      53
Equivalent functions      353
Eratosthenes      511
Erdos      61 339 350 375 377 379 389 391 399 455 461 469 471 477 479
Erdos’s result      379—381
Ergodic measure      52
Ergodic theory      52
Ergodic theory, Riemann hypothesis      52
ERH      see “Extended Riemann hypothesis”
Estimate, $E_1(T)$      146 147
Estimate, $E_2(T)$      146
Estimate, $E_k(T)$      148
Estimate, $N(T) - N_0(T)$      152
Estimate, $R_{2v}$      31
Estimate, $\zeta(s)$, at infinity      455
Estimate, $\zeta(\frac12 + it)$      146
Estimate, coefficient      371
Estimate, N(T)      31 407
Estimate, S(T)      150
Estimate, Z(t)      151
Euclid      319 320
Euclid’s theorem      319 320
Euler      10 29 62 98 124 201 244 299 319 320 342
Euler product      10 11
Euler product formula      see “Euler product”
Euler product, $L(s, \chi)$      111
Euler product, $L(s, \chi_3)$      130
Euler product, $\zeta(s)$      11 16 98 111 124 139 144 201 242 320 322 342 461 463 464
Euler product, $\zeta(s)$, convergence      201
Euler product, $\zeta(s)$, logarithm      16 98
Euler product, $\zeta(s)$, logarithmic derivative      243 322 463 464
Euler product, $\zeta(s, C)$      103
Euler product, Davenport — Heilbronn zeta function lack      144
Euler product, fundamental theorem of arithmetic      11
Euler product, L-function, global      100
Euler product, L-function, primitive waveform      101
Euler product, Z(s)      145
Euler product, zeta function, number field      130
Euler — Maclaurin summation formula      29 38
Euler — MacLaurin summation formula, improvement      32
Euler — MacLaurin summation formula, Riemann — Siegel formula      32
Euler’s constant      48 52 143 244 471
Euler’s constant, Riemann hypothesis      52
Euler’s factorisation formula      457
Euler’s phi function      133 (see “Euler’s totient function”)
Euler’s totient function      48 54 58 514 (see
Evaluation, $\Delta$      286
Evaluation, $\Sigma_{p^m}\dfrac{\log(p)}{p^m}$      290
Evaluation, $\Sigma_{p^m}\log(p)$      282
Evaluation, $\Sigma_{\rho}\dfrac{1}{\sigma^2+t^2}$      247
Evaluation, $\Sigma_{\rho}\dfrac{y^{\sigma-1}}{t^2}$      274
Evaluation, $\Sigma_{\rho}\dfrac{y^{\sigma-1}}{\sigma^2+t^2}$      278
Explicit formula, $\psi(x)$      125 501
Explicit formula, Motohashi      147
Explicit formula, Riemann      104 125
Explicit formula, Weil      104 128 129
Explicit formula, Weil, $\zeta(s)$      104
Explicit formula, Weil, L-function      104
Explicit formula, Weil, zeta function      104
Exponential decay      13 152
Exponential time      512
Extended Riemann hypothesis      57 58 509
Extended Riemann hypothesis, arithmetic progression      63
Extended Riemann hypothesis, consequence      61 63 509 512
Extended Riemann hypothesis, equivalent statement      57 58
Extended Riemann hypothesis, generalized Riemann hypothesis      57
Extended Riemann hypothesis, primality test      509 512
Farey      48
Farey series      48
Farey series, $F_n$      48
Farey series, Haros      48
Farey series, Riemann hypothesis      49
Farey series, term      48
Farmer      132
Fast Fourier transform algorithm      see “Algorithms”
Fejer      339 350
Fermat      319 511
Fermat’s Last Theorem      4 101 111 126
Fermat’s Little Theorem      114 319 511 512
Fermat’s little theorem, extension      319
Fermat’s little theorem, finite field, primality test      512
Fermat’s little theorem, generalization      512 513
Fermat’s little theorem, polynomial ring, finite field      512
Fermat’s little theorem, primality test      511 512
FFT      see “Fast Fourier transform”
Field      see “Finite field” “Function “Number
Field, algebraic closure      336
Field, algebraically closed      105
Field, Galois      336
Field, imaginary quadratic      133
Fields medal      27 333
Finite field      102 103 115 131 335 512 514 517
Finite field, $F_p$      514 517
Finite field, $F_q$      102 103
Finite field, polynomial ring      512
Fixed point formula      104
Flow      52
Flow, horocyclic      52
Form factor      437 442
Forme quadratique      233
Formule, Cahen      313
Formule, Gauss      244 251 257
Formule, Legendre      183 185 189
Formule, Riemann      313
Fourier analysis      455
Fourier integral      462
Fourier inversion      99
Fourier transform      51 127 128 152 440 455 491 502
Fourier transform of $\Xi(t)$      127
Fourier’s theorem      205
Fouvry      520
Fractional part      12 30 52 127 {x}”)
Frey      111
Friedlander      134
Frobenius endomorphism      103 105
Frobenius endomorphism, cohomology group      115
Frobenius endomorphism, eigenvalue      103 115
Frobenius endomorphism, fixed point      104
Frobenius endomorphism, Lefschetz fixed point formula      104
Frobenius endomorphism, trace      104
Fujii      155 498
Function field      333 335
Function field, Riemann hypothesis      333 335
Function, elliptique      314
Function, Mobius      471
Function, Riemann      213 235 237 238 242
Function, Schlomilch      217
Function, Von Mangoldt      471
Functional analysis      127 211
Functional equation, $L(s, \chi)$      112
Functional equation, $L(s, \chi_3)$      130
Functional equation, $L(s, \Delta)$      59 112
Functional equation, $L_E(s)$      130
Functional equation, $L_v(s)$      222
Functional equation, $L_{\Delta}(s)$      130
Functional equation, $\Lambda(s, \pi)$      59 113
Functional equation, $\mu(\sigma)$      149
Functional equation, $\vartheta(t)$      13 25
Functional equation, $\xi(s)$      14 20
Functional equation, $\zeta(s)$      14 15 97—99 111 123 139 202 203 294 322 342
Functional equation, $\zeta(s)$, logarithmic derivative      444
Functional equation, $\zeta(s)$, symmetric      123 158
Functional equation, $\zeta(s, C)$      103
Functional equation, $\zeta_K(s)$      337
Functional equation, alternating zeta function      98
Functional equation, approximate      32 33 126
Functional equation, Davenport — Heilbronn zeta function      144
Functional equation, L-function, elliptic curve      100
Functional equation, L-function, global      100
Functional equation, L-function, primitive waveform      101
Functional equation, Z(s)      145
Functional equation, zeta function, number field      130
Functions      see “L-functions” “Arithmetic “Convolution “Dirichlet “Mean” “Partial “Schlomilch “Zeta
Functions, $A*_T(u)$      429 431
Functions, $B_n(x)$      30
Functions, $E_k(T)$      145
Functions, $E_m$      33
Functions, $F(y, \lambda)$      419 423
Functions, $F(\alpha)$      437 439
Functions, $F(\alpha, T)$      437 439
Functions, $H(\lambda, z)$      51
Functions, $I_1$      153 160
Functions, $I_1(T)$      67
Functions, $I_2$      153 160
Functions, $I_2(T)$      67
Functions, $I_k(T)$      66 67 131
Functions, $J_{\mu}(x)$      225
Functions, $L(s, \Delta)$      59
Functions, $log(\zeta(s))$      16 99 204 213 214 216 322
Functions, $log(\zeta(s))$, real part      214
Functions, $log(\zeta(s))$, singularity      99
Functions, $L_1(x)$      365
Functions, $L_p(s)$      57
Functions, $N(\alpha, T)$      102
Functions, $N(\sigma, T)$      65 146
Functions, $N_0(T)$      125 152
Functions, $N_1(T)$      38
Functions, $N_M(T)$      152
Functions, $S_1(T)$      65 66
Functions, $S_M(T)$      155
Functions, $Z^{(k)}(t)$      151
Functions, $Z_2(\xi)$      147
Functions, $[x, x_1, ... , x_n]$      154
Functions, $\chi(s)$      32 139
Functions, $\Delta$      20 128 284
Functions, $\Delta(t)$      158
Functions, $\Delta(x)$      148
Functions, $\Delta(z)$      59 112 130
Functions, $\Delta^{(k)}(t)$      158
Functions, $\Delta_2(x)$      148
Functions, $\Delta_k(x)$      148
Functions, $\dfrac1{\zeta(s)}$      49 125 140 299
Functions, $\dfrac1{\zeta(s)}$, derivative      299
Functions, $\dfrac{\Gamma'(a)}{\Gamma(a)}$      245 251
Functions, $\dfrac{\Gamma'(s)}{\Gamma(s)}$      22
Functions, $\dfrac{\log(\zeta(s))}{s}$      205
Functions, $\dfrac{\xi'(s)}{\xi(s)}$      50
Functions, $\dfrac{\xi'(s)}{\xi(s)}$, Riemann hypothesis      50
Functions, $\dfrac{\xi(s)}{\xi(s)}$,      21 22
Functions, $\dfrac{\zeta'(s)}{\zeta(s)}$      22 23 227 229 243 259 322
Functions, $\dfrac{\zeta'(s)}{\zeta(s)}$, s = 0      282 293
Functions, $\dfrac{\zeta'(s)}{\zeta^2(s)}$      299
Functions, $\eta(s)$      49
Functions, $\Gamma(s)$      12 13 15 22 26 111 124
Functions, $\Lambda(s)$      111
Functions, $\Lambda(s, \Delta)$      112
Functions, $\log (\xi(t))$      204
Functions, $\log((s - 1)\zeta(s))$      98
Functions, $\log(\Gamma(a))$      245
Functions, $\log(\Gamma(s))$      21
Functions, $\mathfrak{R}(\log(\zeta(s)))$      16
Functions, $\mathfrak{R}\left(\dfrac{\Gamma'(a)}{\Gamma(a)}\right)$      247
Functions, $\mathfrak{R}\left(\dfrac{\zeta'(s)}{\zeta(s)}\right)$      22
Functions, $\mu(\sigma)$      148
Functions, $\phi$      103
Functions, $\Phi(t)$      51 127
Functions, $\Pi(s - 1)$      201
Functions, $\pi(x) - Li(x)$      142 403 405
Functions, $\Pi(x)$      99 406 410
Functions, $\pi(x;k, l)$      57 58 63 133
Functions, $\Pi_0(x)$      406 407 417
Functions, $\pi_2(x, k)$      497
Functions, $\psi(x)$      98 125 323 325 327 328 406 408 463 465 487
Functions, $\psi_0(x)$      406 408
Functions, $\psi_1(x)$      409
Functions, $\psi_{\mu}(x)$      227
Functions, $\sigma(y)$      281 282 285 287 289 297
Functions, $\sin\theta(t)$      33
Functions, $\theta(t)$      32 33 158
Functions, $\theta(x)$      321
Functions, $\varphi(u, t)$      262
Functions, $\varphi(x)$      173 220
Functions, $\vartheta(t)$      
13 25 26
Functions, $\vartheta(x)$      98 379 392
Functions, $\Xi(iz)$      51
Functions, $\xi(s)$      14 19—22 25—27 31 38 50 97 124 143 313
Functions, $\xi(s, \chi_3)$      130
Functions, $\xi(t)$      38
Functions, $\xi(\frac12 + it)$      313
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