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| Elliot P.D.T.A. — Probabilistic Number Theory One |
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| Предметный указатель |
 -norm 12 23
Abel 352
Abundant numbers 3—4 189
Aczel 76
Additive function, finitely distributed 258 259 260 267 270 275 276 283
Additive function, finitely distributed (definition) 11
Adjoint of operator 181—182
Akilov and Kantorovich 181
Algebra of sets 29—30 115—146
Analytic characteristic functions 57 112—113
Asymptotic density 295 297;
asymptotic relations 19—21
Bakstys 280
Banach — Hahn 181
Barban 9 12 80 92 93 136 184
Barban and Vinogradov 122 126
Barban, Vinogradov and Levin 174
Basis 294
Behrend 4 189 214
bernoulli 36
Berry 74 78
Berry — Esseen 74 101 117 217
Berry — Esseen theorem 74 117
Bertrand 3
Bessel — Hagen 3 4 189
Billingsley 30
Birch 14
Bombieri 12 90 92 93 184 185 186 317
Bombieri and Davenport 185
Borel 3
Borel — Cantelli 45 46
Borel — Cantelli lemma, applications 45—46
Borel — Caratheodory 58
Borel — Caratheodory lemma 58
Brownian motion 3
Brun 4 9 80 134 184 210 213
Brun — Titchmarsh 90 120 135 160 161 213
Brun's sieve 4 9 80 129
Burgess 154 157
Cantelli — Borel 45 46
Caratheodory — Borel 58
Cartwright 94
Cauchy 7 14 17 20 46 76 231 239 283 289 290 329
Cauchy law 14
Cauchy — Schwarz 42 68 135 149 150 151 160 161 164 168 174 196 197 201 202 234 243 246 271 300 304 317 338 339 345 348 349
Cauchy's functional equation 17 20 76 283 289
Central limit theorem 218
Character, Dirichlet 110—111
Character, Dirichlet, primitive 110
Characteristic function 27
Characteristic function (definition) 9
Characteristic function, analytic 57 112—113
Characteristic function, component of 113—114
Characteristic function, convergence of 28
Chowla, S. 4 189
Circle method 2 6—9
Class Number, quadratic 14 110—111 117
Classification 13
Coefficients, Fourier 66
Compactness lemma 25
Component of characteristic function 113—114
Component of distribution function 113
Concentration function 31 217—218
Conditional probability 31 35
conjugate 12 181—182
Continuity criterion, Levy's 46 78
Continuity of distribution function 48—49
Control, mathematical 13
Convergence, characteristic functions 28
Convergence, Fourier coefficients 67—68
Convergence, Mellin — Stieltjes transforms 63
Convergence, modified-weak 273—274 280
Convergence, modified-weak (definition) 63
Convergence, weak 24—30
Convolution 30 254—255
Convolutions, infinite 37
Courant — Fisher 163
Courant — Fisher theorem 163—164
Cyclotomic field 114
Daboussi and Delange 358
Davenport 4 111 189 214
Davenport and Bombieri 185
Davenport and Halberstam 12 185
de Bruijn 77
de Bruijn, van Aardenne-Ehrenfest and Korevaar 18 77
de la Vallee-Poussin 1 29
Decomposition 13
Dedekind 114
Dedekind — Dirichlet series 114
Delange 10 11 218 219 225 226 254 256 258 283 285 286 301 305 333
Delange and Daboussi 358
Density asymptotic see ”Notation”
Density, lower=density, lower asymptotic 295 297
Density, Schnirelmann 77 293
Desargues 12
Desargues' theorem 12
diamond 219
Differences 16
Differential equation, approximate 13
Dirichlet 10 12 14 15 79 92 94 96 98 100 101 108 109 110 111 112 114 183 184 186 222 224 225 235 301 308 311 317 322 326 331 335 337 341 342 348 356
Dirichlet L-series 14
Dirichlet series 79 94
Dirichlet series component 114
Dirichlet series operator 186
Dirichlet, marriage of 111—112
Dirichlet, multiplication, convolution 98 109
Discriminant of quadratic field 110—111
Discriminant, fundamental 111
Dispersion method 93
Distribution function 24
Distribution function convergence 24 25
Distribution function improper 25
Distribution function proper 25
Distribution function, continuity of 48—49
Distribution functions (mod 1) 65
Distribution functions (mod 1) convergence 65—68
Distribution functions (mod 1) discontinuous, quantitative Fourier inversion 75—76
Distribution functions (mod 1), continuity of 67
Distribution law 24
Doeblin 217
Dual 12 13
Dual of operator 12 181—182
Dual of Turan — Kubilius inequality 13 147—186 194 335
Dual space 181—182
Duality principle 150 162 185—186 316—317
Edwards 68
Egoroff 18
Einstein 3
Elliott 12 13 75 76 144 153 155 185 217 218 219 269 283 286 292 295 333
Elliott and Ryavec 10 257 258 265 268 283 306
Eratosthenes 221 254 266
Erdoes 3 4 5 10 11 90 91 118 187 189 203 207 210 211 212 213 214 218 219 220 254 258 265 283 285 301 302
Erdoes and Kac 4 5 14 146 182 214
Erdoes and Ryavec 268
Erdoes and Selberg 10 256
Erdoes and Turan 75
Erdoes and Turan inequality 75
Erdoes and Wintner 4 10 187 214 254 280
Erdoes — Kac — Kubilius 9
Erdos — Wintner theorem 187—224
Erdos' sample paper 207—210
Erdos' sample paper, commentary on 210—213
Esseen 74 78 203 218
Esseen — Berry 74 101 117 217
Esseen — Berry theorem 74 117
Esseen's inequality 74
Euclid 4
Euler 89 95 96 97 114 134 188 203 230 326 338 341 349 353
Euler product 95 97 114 230 326 338 341 349 353
Euler's constant 89
| Euler's function, distribution of 188—189 213 214
Fainleib 74 75 203 219
Fainleib and Levin 11 286
Fejer 3 70 78 101 229
Fejer kernel 78 101 229
Feller — Lindeberg 56
Feller — Lindeberg condition 56
Finite probability space 5 115—146
Finitely distributed additive function 258 259 260 267 270 275 276 283
Finitely distributed additive function (definition) 11
Finitely monotonic additive function 268—269
Fisher — Courant 163
Fisher — Courant theorem 163—164
Forti and Viola 12 185 186 317
Fourier coefficients 66
Fourier inversion (mod 1), quantitative 74—76
Fourier inversion, quantitative 69
Fourier — Stieltjes 61 305
Fourier — Stieltjes transform 61; see also “Characteristic Function”
Frechet — Shohat 59 78
Frechet — Shohat — Wintner 59—60 78
Functional equation, Cauchy's 17 20 76 283 289
Functions, slowly oscillating 18
Fundamental lemma 80
Galambos 218 280 281
Gallagher 12 93 185
Gauss 1 51 94
Gaussian component 51 94
Geometry, Plane Projective 12
Gershgorin 165 316
Gershgorin discs 165 316
Gnedenko 53 55 56
Gnedenko and Kolmogorov 24 26 28 29 49 50 51 53 54 55 56 57
Group of substitutions 13
hadamard 1 29
Hahn — Banach 181
Halasz 10 12 21 77 114 224 225 226 233 252 255 256 286 308 3 3 330 33
Halberstam 6
Halberstam and Davenport 12 185
Halberstam and Richert 80 185
Halberstam and Roth 77
Hamel 76
Hardy 1 3 102
Hardy and Ramanujan 2 3 5 13 14
Hardy and Wright 85 89 108 112 118 133 134 224
Hardy — Littlewood (Hardy and Littlewood) 2 77 102 254 348 351 358
Hardy — Littlewood circle method 2 6—9
Hardy — Littlewood tauberian theorem 102 254 348 351 358
Hardy — Littlewood tauberian theorem (statement) 77
Hardy, Littlewood and Polya 186
Hartman 292
Heilbronn 94 114
Hengartner and Theodorescu 218
hermite 12 162 166
Hermitian matrix, operator 162
Hermitian operator 12
Hermitian operator, spectral radius 12 162
Highest common divisor of a sequence 295
hilbert 181 185
Hilbert's inequality 185
Hoelder 179 186 236 313 329
Ibragimov and Linnik 78
Ikehara — Wiener 100 101 102
Improper distribution function 25
Independence and divisibility by primes 146
Independence in probabilistic number theory 4 146
Independent random variables 30
Infinite convolutions 37
Infinitely divisible law 49
Infinitely divisible law characteristic function according to Kolmogorov 51
Infinitely divisible law characteristic function according to Levy — Khinchine 49—50
Infinitely divisible laws, convergence of 53
Infinitesimal variable 54
Integral equation, approximate 11
Inversion formula 28
Jessen and Wintner 46 78 193
Kac 4 5 146
Kac — Erdoes (Kac and Erdos) 4 5 14 146 182 214
Kac — Kubilius — Erdos 9
Kantorovich and Akilov 181
Karamata 18 77
Kesten 218
Khinchine 55 77
Khinchine and Levy 49 57
Khinchine — Levy representation 49—50 57
Kobayashi 12 185
Kolmogorov 3 32 44 45 51 52 53 56 77 217
Kolmogorov and Gnedenko 24 26 28 29 49 50 51 53 54 55 56 57
Kolmogorov's inequality 44
Korevaar, van Aardenne-Ehrenfest and de Bruijn 18 77
kronecker 110 111
Kronecker symbol 110—111
Kronecker symbol primitive character 110
Kubilius 5 6 11 80 115 119 122 123 125 126 128 129 138 139 140 142 144 145 146 147 148 180 181 258 286
Kubilius — Erdoes — Kac 9
Kubilius — Tunin inequality 6 13 147—186 192 199
Kubilius — Tunin inequality dual of 13 147—186 194 335
Kubilius — Turan 6 13 147 152 158 173 182 185 192 199 218
Kubilius' model 115—146
Kubilius' model, construction of 119
Kuipers and Niederreiter 78
Kummer 111
L-series, Dirichlet 14 110—111 114
Lambert 219
Lambert series 219
Landau 1 94 111 254
Landau and Walfisz 100
Lang 101
Large deviation inequality for random variables 127
Large sieve 9 10 12 13 93 165 183—186 317
Law, Cauchy 14
Law, normal 52
Law, normal (definition) 11
Law, Poisson 52—53
Law, stable 11
Laws on a finite interval 58
Lebesgue 16 19 21 22 23 48 59 67 107 222 228 258 260 359
Lebesgue -class 22
legendre 110 154
Legendre symbol 110 154
LeVeque 6 75 76
LeVeque's conjecture 6
Levin and Fainleib 11 286
Levin and Timofeev 10 12 257 258
Levin, Timofeev and Tuliaganov 274 275 280 281
Levy 3 14 24 25 3 46 50 51 52 53 57 78 193 195 217 219
Levy and Khinchine 49 57
Levy metric (distance) 14 24
Levy representation (formula) 50
Levy representation (modified) 51
Levy — Khinchine representation 49—50 57
Levy's continuity criterion 46 78
Leyin, Barban and Vinogradov 174
Liapounoff 218
Limit law 24
Limiting distribution of a strongly additive function 4
Lindeberg — Feller 56
Lindeberg — Feller condition 56
Linnik 8 9 58 78 93 112 113 183 184 218 317
Linnik and Ibragimov 78
Littlewood and Offord 217
Littlewood — Hardy (Littlewood and Hardy) 2 77 102 254 348 351 358
Littlewood, Polya and Hardy 186
Loeve 127
Lubell 78
Lukacs 78
Major Arcs, intervals 7
Mann 77 293
Mann's theorem 77 293
Manstavicius 286 305
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