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

Functions, $\xi_E(s)$       130
Functions, $\xi_k(s)$       217 218
Functions, $\xi_{\Delta}$       130
Functions, $\zeta'(s)$       49
Functions, $\zeta(\frac12 +it)$       102 123 126 132 139
Functions, A(u)      429 431
Functions, F(x)      204 241 292
Functions, F(X, T)      485 488 498
Functions, G      157 (see also “Barnes’s G function”)
Functions, H(z)      26 27
Functions, I      153 163
Functions, J(X, T)      502
Functions, k      155 164
Functions, k(t, H)      155
Functions, k(t, T)      164
Functions, k-tuple correlation      442
Functions, L(x)      355 429 431
Functions, Li(x)      18 46 58 98 140 171 208 235 239 295 403 405 417
Functions, ln(x)      514
Functions, log (x)      469 514
Functions, log(s - 1)      224
Functions, M(x)      47 69 125 325 327 328 433 469 471 472 483
Functions, N(T)      9 15 19—21 24 31 35 38 41 101 125 140 407 498
Functions, pair correlation      437 442
Functions, R(T)      407
Functions, R(t, x)      159
Functions, R(x)      384 385
Functions, S(N)      35
Functions, S(T)      125 140
Functions, S(t, x)      159
Functions, S(\hat{t})      116
Functions, U      163
Functions, Z(t)      32 33 35 141—143 150 151 158 159
Functions, Z(t), even      141
Functions, Z(t), logarithmic derivative      143
Functions, Z(t), real      141
Functions, [x]      12 464
Functions, {x}      12 30 52
Fundamental Theorem of Arithmetic      10 124
Fundamental theorem of arithmetic, analytic form      11
Fundamental theorem of arithmetic, Euler product      11
Gallagher      488 490 495
Galois field      336
Gamma function      12 13 15 22 26 111 124
Gamma function, logarithmic derivative      22
Gauss      43 46 98 124 133 142 193 201 209 239 244 251 257 319 321 322 461
Gauss measure      130
Gauss sum      113
Gauss sum, sign      112
Gaussian unitary ensemble      40 42 115 130
Gaussian unitary ensemble conjecture      131
Gaussian unitary ensemble, eigenvalue      42
Gaussian unitary ensemble, eigenvalue spacing      42
Gaussian unitary ensemble, eigenvalue, normalized      42
Gauss’s class number problem      133
Gauss’s conjecture      124 125
Gauss’s conjecture, proof      133
Gauss’s conjecture, restatement      125
Gauss’s Formula      244 251 257
Gelfand      151
Gelfond      126 155
General divisor function      148 (see also “Arithmetic functions
General linear group      58 112
Generalized Riemann hypothesis      64
Generalized Riemann hypothesis, Artin’s primitive root conjecture      64 520
Generalized Riemann hypothesis, consequence      62 64
Generalized Riemann hypothesis, extended Riemann hypothesis      57
Generalized Riemann hypothesis, Goldbach’s conjecture      62
Generalized Riemann hypothesis, Miller — Rabin primality test      63
Generalized Riemann hypothesis, primality test      63
Generalized Riemann hypothesis, Riemann hypothesis      57
Generalized Riemann hypothesis, Solovay — Strassen primality test      63
Generic point      335
Genus      103 336
Geodesic      129
Geodesic motion      114
Geodesic motion, surface      114
Germain      512 520
Ghosh      67 131
Gilbert      235
GLH      see “Grand Lindelof hypothesis”
Goldbach      62 319
Goldbach conjecture      62 319
Goldbach conjecture, strong      62
Goldbach conjecture, weak      62
Goldbach type      114
Goldfeld      134 520
Goldschmidt      209
Goldston      485 487 489 498
Goldwasser      512
Goldwasser — Kilian primality testing algorithm      512
Gonek      131
Goursat      211
Gram      29 33 34 299
Gram block      34
Gram block, consecutive      34
Gram point      33 34
Gram point, bad      34
Gram point, good      34
Gram’s law      33 34 443
Gram’s law, exception      34
Grand Lindelof hypothesis      113
Grand Lindelof hypothesis, approximation      114
Grand Lindelof hypothesis, consequence      113
Grand Riemann hypothesis      58—60 109 111 113
Grand Riemann hypothesis, $\Lambda(s, \pi)$       117
Grand Riemann hypothesis, approximation      114 115
Grand Riemann hypothesis, consequence      111 113 448
Grand Riemann hypothesis, Dirichlet L-functions      114
Grand Riemann hypothesis, Dirichlet L-functions, consequence      114
Grand Riemann hypothesis, verification      116
Graph      53
Graph of Z(t)      150
Graph theory      53
Graph, adjacency matrix      53
Graph, cycle      53
GRH      see “Grand Riemann hypothesis”
Gronwall      361
Gronwall’s inequality      361
Gross      134
Grothendieck      103
Group,       112
Group, $GL_m(\mathbb{A})$       58 112
Group, $GL_m(\mathbb{Q})$       112
Group,       53
Group, $\Gamma_0(N)$       100 101
Group, $\mathfrak{G}$       517
Group, $\mathfrak{G}$ , cardinality      517 518
Group, cohomology      115
Group, conjugacy class      145
Group, Div(C)      102
Group, divisor      102 103 105
Group, element      53
Group, element, order      53
Group, G      517
Group, G, cardinality      517 518
Group, general linear      58 112
Group, Hecke      100
Group, ideles      116
Group, modular      112 147
Group, monodromy      115
Group, rational points, elliptic curve      135
Group, semi-simple      116
Group, SL(2, \mathbb{Z})      128
Group, symmetric      53
GUE      see “Gaussian unitary ensemble”
GUE conjecture      131
Gupta      64 374
Haar measure      131 132
Haas      129

hadamard      15 47 61 114 125 211 213 218 228 235 238 241 317 322 323 333 455 461
Hadamard product representation      21
Hadamard product representation, logarithmic derivative      21
Hadamard — de la Vallee Poussin theorem      211 235
Hafner      146
Halasz      484
Halberstam      497
Halphen      225 231 232
Halphen’s theorem      225 231 232
Hamiltonian      114
Hamiltonian, eigenstate      114
Hardy      9 24 31 32 51 62 67 98 114 126 129 131 146 311 313 317 319 325 327 495
Hardy and Littlewood, Riemann hypothesis      51
Hardy’s function      31
Hardy’s theorem      24 27
Hardy’s theorem, proof      27
Hardy’s theorem, Riemann hypothesis      24 27
Hardy’s Z-function      32 33 35
Harmonic form      105
Harmonic number      48
Harmonic series      10 11 16
Haros      48
Haros, Farey series      48
Haselgrove      429 431 432
Hasse      103
Hasse — Weil L-function      130 135
Heath — Brown      63 64 72 102 489
Heath — Brown’s theorem      64
Heath — Brown’s theorem, Artin’s primitive root conjecture      64
Hecke      130 133
Hecke group      100
Hecke operator      101
Hecke operator, eigenvalue      101
Heilbronn      133 144
Heins      455 462
Hejhal      127 129 144
hermite      211
Hermitian linear operator      437 442
Hermitian matrix      130 131 437 442 443
Hermitian matrix, eigenvalue      130 131 437 442
Hermitian operator      40 127
Hermitian operator, eigenvalue      40 127
Heuristics      137
hilbert      4 37 40 52 105 115 123 126 127 130
Hilbert space      116
Hilbert space, L-functions      116
Hilbert — Polya conjecture      40 (see also “Conjectures”)
Hilbert — Schmidt integral operator      52
Hilbert — Schmidt integral operator, Riemann hypothesis      52
Hildebrand      475 477
Hodge      105
Hodge’s theorem      105
Hooley      64 100
Horocyclic flow      52
Huang      512
Hudson      44
Hurwitz      144 217 219 222 348
Hurwitz zeta function      144 (see also “Zeta functions a)$"/>”)
Hurwitz’s theorem      348
Hutchinson      29 34
Huxley      146
Hyperbolic Laplacian      101
Hypothesis H      44 403 406 409
Hypothesis H, consequence      403 406 407 409—411 413 415 417 424
Hypothesis H, Riemann hypothesis      44
Ideal      58
Ideal class      133
Idele class group      116
Ikehara      455 459 462
Ikehara — Wiener Tauberian theorem      459 462
Ikehara — Wiener Tauberian theorem, prime number theorem      459 462
Ikehara — Wiener Tauberian theorem, “poor man’s” version      459 462
Imaginary quadratic field      133
Inegalite de Selberg      471
Infimum, $1 - \sigma_n$       241 261 265 270
Infimum, $M(n)n^{\frac12}$       70
Infimum, $M(n)n^{\frac12}$ , upper bound      70
Infimum, $\dfrac{M(x)}{x}$       471
Infimum, zeros, imaginary parts      441 443
Ingham      67 126 131 311 405 412 429 431 433 453 455 462
Ingham’s convergence theorem      455
Ingham’s convergence theorem, proof      455—457
Ingham’s exponent      102
Ingham’s theorem      453
Ingham’s theorem, proof, Newman      453
Integer ring      514
Integer ring, $\mathcal{O}_K$       58
Integer, introspective      516 517
Integer, introspective, closed under multiplication      516 517
Integer, introspective, residue      517
Integer, introspective, set      517
Integer, modulo n      514 517
Integer, modulo n, residue      517
Integer, odd      51
Integer, square      64
Integer, sum, prime numbers      62
Integral ideal      58
Integral ideal, norm      58
Integral operator      52
Integral part      12 (see “Functions [x]”)
Integral representation, $M_{Z,f}(t)$       151
Integral representation, $M_{Z,f}^{(k)}(t)$       151
Integral representation, $Z_2(\xi)$       147
Integral representation,       154
Integral representation, $\dfrac{\Gamma'(a)}{\Gamma(a)}$       245 251
Integral representation, $\dfrac{\log(\zeta(s))}{s}$       205
Integral representation, $\dfrac{\zeta'(s)}{\zeta(s)}$       465
Integral representation, $\Gamma(s)$       13
Integral representation, $\log(\Gamma(a))$       245
Integral representation, $\Pi(s - 1)\zeta(s)$       202
Integral representation, $\psi(x)$       323
Integral representation, $\xi(t)$       203
Integral representation, $\xi_k(s)$       218
Integral representation, $\zeta(s)$       12 98 99 464
Integral representation, F(X, T)      498
Integral representation, Li (x)      46 58 140 239 295 405
Integral representation, N(T)      101
Intermediate Value Theorem      38
Internet security      509
Intersection number      335 336
Introspective      516 517
Introspective, polynomial      516
Inverse Fourier transform      157
inversion      208
Inversion formula      99
Irreducible correspondence      335
Irreducible polynomial      514 517
Irreducible representation, unitary      58 112
Isogenous      114
Ivic      102 137 139 146—148 151
Iwaniec      100 117 121 133 134
jacobi      193 203 335 512
Jacobi symbol      512 (see also “Arithmetic functions
Jacobi symbol, primality test      512
Jacobi theta function      13 25 26
Jacobi’s inversion theorem      335
Jensen mean      352 375
Jessen      346 373
Jutila      150
Kalai      518
Karatsuba      144
Katz      105 131 132
Kayal      63 509 511
Keating      67 115 131 132
Keating — Snaith conjecture      115 131 132
Kilian      512
Klein      141
Knopp      345
Korevaar      61 459 461
Korobov      18

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