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Elliot P.D.T.A. — Probabilistic Number Theory Two: Central Limit Theorems
Elliot P.D.T.A. — Probabilistic Number Theory Two: Central Limit Theorems

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Название: Probabilistic Number Theory Two: Central Limit Theorems

Автор: Elliot P.D.T.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 375

Добавлена в каталог: 13.09.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^{2}$-norm      12 23
$\mathbb{Z}$-module      289 340
Abel      352 239 243
Abel’s lemma      239 243
Abundant numbers      3 4 189
Acz$\acute{e}$l      76
Additive function, finitely distributed      11 259 260 267 270 275 275 283
Additive function, finitely distributed (definition)      258
Adjoint of operator      181 182
Akilov and Kantorovich      181
Algebra of sets      29 30 115 146
Analytic characteristic functions      57 112
Asymptotic density      98 100 109
asymptotic relations      19 21
Axer      239 240 241 243 244 261
Axer’s lemma      239 240 241 243 242 261
Babu      288 330
Bakstys      280
Banach — Hahn      181
Barban      9 12 80 92 93 136 184 27 40 41 44 50 51 263 268 269 329
Barban and A.I. Vinogradov      122 126 263
Barban — Vinogradov — Bombieri      51 269
Barban, Vinogradov and Levin      174 27 50
Basis      294
Bateman      261
Behrend      4 189 214
bernoulli      36
Berry      74 78 22
Berry — Esseen      74 101 117 217 22 266 269
Berry — Esseen theorem      74 117 22 265 269
Bertrand      3
Bessel — Hagen      3 4 189
Billingsley      30 288
Birch      14 98 99 120
Bohr H., address to      1950
Bohr, H.      248
Bombieri      12 90 92 93 184 185 186 317 261
Bombieri and Davenport      185
Bombieri — Barban — Vinogradov      51 269
Borel      3 170
Borel — Cantelli      45 46
Borel — Cantelli lemma, applications      45 46
Borel — Carath$\acute{e}$odory      58
Borel — Carath$\acute{e}$odory lemma      58
Borel — Heine      168
Brownian motion      3 288
Brun      4 9 80 134 184 210 213 21 24 25 44
Brun — Titchmarsh      90 120 135 160 161 213 32
Brun’s Sieve      4 9 80 129 21 25 44
Burgess      154 157 339
Cantelli — Borel      45 46
Carath$\acute{e}$odory — Borel      58
Cartwright      94
Cauchy      7 14 17 20 46 76 231 239 283 289 290 329 10 13 136 137 143 144 179 192 228 293 297 340 341
Cauchy law      14 136 143
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 28 42 43 57 117 220 259 278 283
Cauchy’s functional equation      17 20 76 283 289 179 340
Central limit theorem      218 18 24
Character, Dirichlet      110 — 111 178 222 241 313 338 339
Character, primitive      110 320
Characteristic exponent of stable law      135 142
Characteristic function      9
Characteristic function, (definition)      27
Characteristic function, analytic      57 112
Characteristic function, component of      113 114
Characteristic function, convergence of      28
Chowla and Erd$\ddot{o}$s      314 329
Chowla, S.      4 189
Circle method      2 6
Class $H$, additive functions      12 14 17 27 29 30 38 53 125 336
Class $L$ of Khinchine      125 167 169
Class $M$, laws      148 161 164 173 337
Class Number, quadratic      14 110 117 313
Classification      13
Coefficients, Fourier      66
Compactness lemma      25
Component of characteristic function      113 — 114
Component of distribution function      113 168
Concentration function      31 217 218
Conditional probability      31 35
Congress Math      248
conjugate      12 181
Continued fraction, periodic      138
Continuity criterion, L$\acute{e}$vy’s      46 78
Continuity of distribution function      48 49
Control, mathematical      13
Convergence, (definition)      273 — 274 280
Convergence, characteristic functions      28
Convergence, Fourier coefficients      67 68
Convergence, Mellin — Stieltjes transforms      63
Convergence, modified-weak      63
Convergence, weak      24 30
Convolution      30 254 255
Convolutions, infinite      37
Copenhagen lecture      248
Courant — Fisher      163
Courant — Fisher theorem      163 164
Cyclotomic field      114
Daboussi and Delange      358
Davenport      4 111 189 214 24 320
Davenport and Bombieri      185
Davenport and Halbertstam      12 185
de Bruijn      77
de Bruijn, van Aardenne — Ehrenfest and Korevaar      18 77
de la Vall$\acute{e}$e Poussin      1 29 261
Decomposition      13
Decomposition of $\alpha(x)$      58 59 60 86
Dedekind      114
Dedekind — Dirichlet series      114
Delange      10 11 218 219 225 226 254 256 258 283 285 286 301 305 333 51 255 287 311 333
Delange and Daboussi      358
Density, asymptotic      98 100 109
Density, lower = density, lower asymptotic      295 297
Density, Schnirelmann      77 293
Desargues      12
Desargues’ theorem      12
diamond      219
Diamond and Steinig      261
Differences      16
Differential equation, approximate      13 75 80
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 51 71 83 125 139 178 187 211 218 221 222 230 240 241 242 243 245 246 260 277 286 301 313 324 339
Dirichlet $L$-series      14 110 111 114 241 313
Dirichlet character      178 222 241 313 338 339
Dirichlet multiplication, convolution      98 109 277 301
Dirichlet, marriage of      111 112
Dirichlet-series      79 94
Dirichlet-series component      114
Dirichlet-series operator      186
Discriminant, fundamental      111 319
Discriminant, of quadratic field      110 111 313
Dispersion method      93 40
Distribution function      24
Distribution function, continuity of      48 49
Distribution function, convergence      24 25
Distribution function, improper      25
Distribution function, proper      25
Distribution functions (mod1)      65
Distribution functions (mod1) convergence      65 68
Distribution functions (mod1) discontinuous, quantitative Fourier inversion      75 76
Distribution functions (mod1), continuity of      67
Distribution law      24
Doeblin      2 7
Dual      12 13
Dual of operator      72 181
Dual of Tur$\acute{a}$n — Kubilius inequality      13 147 194 335 55 114
Dual space      181 182
Duality principle      150 162 185 316 315
Edwards      68
Egoroff      18 91
Einstein      3
Elliott      12 13 75 76 144 153 155 185 217 218 219 269 283 286 292 295 333 8 37 48 52 58 60 93 99 101 103 110 112 120 122 123 125 147 148 180 184 208 209 247 286 289 314 328 329 331 334 338
Elliott and Halberstam      272
Elliott and Ryavec      10 257 258 265 268 283 306 169
Eratosthenes      221 254 266
Erd$\ddot{o}$s      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 18 19 20 21 23 24 25 26 99 119 120 202 203 205 206 207 248 249 250 253 329 330 331 332 335
Erd$\ddot{o}$s and Chowla      314 329
Erd$\ddot{o}$s and Kac      4 5 14 146 182 214 12 18 20 24 25 26 262 302
Erd$\ddot{o}$s and R$\acute{e}$nyi      333
Erd$\ddot{o}$s and Ryavec      268
Erd$\ddot{o}$s and Selberg      10 256 211 248 258
Erd$\ddot{o}$s and Selberg, elementary proof of P.N.T.      248 — 253
Erd$\ddot{o}$s and Tur$\acute{a}$n      75
Erd$\ddot{o}$s and Tur$\acute{a}$n inequality      75
Erd$\ddot{o}$s and Wintner      4 10 187 214 254 280 24 172 260 332 335
Erd$\ddot{o}$s at Kac’ lecture      24 25
Erd$\ddot{o}$s — Kac theorem      18 262
Erd$\ddot{o}$s — Kac — Kubilius      9 31 48 125
Erd$\ddot{o}$s — Wintner theorem      187 224
Erd$\ddot{o}$s, Ruzsa and S$\acute{a}$rk$\ddot{o}$zy      290 296
Erd$\ddot{o}$s’ sample paper      207 210
Erd$\ddot{o}$s’ sample paper, commentary on      210 213
Esseen      74 78 203 218 22 274 283 327
Esseen — Berry      74 101 117 217 22 266 269
Esseen — Berry theorem      74 117 22 266 269
Esseen’s inequality      74
Euclid      4
Euler      89 95 96 97 114 134 188 203 230 326 338 341 349 353 76 79 80 82 84 196 277 287 301 314 320 339
Euler product      95 97 114 230 326 338 341 349 353 76 79 80 82 84 196 277 301 314 320 339
Euler’s constant      89
Euler’s function, distribution of      188 — 189 213 214
Fa$\breve {\iota}$nle$\breve {\iota}$b      74 75 203 219
Fa$\breve {\iota}$nle$\breve {\iota}$b and Levin      11 286 145
Fa$\breve {\iota}$nle$\breve {\iota}$b and Toleuov      46 51
Fej$\acute{e}$r      3 70 78 101 229
Fej$\acute{e}$r kernel      78 101 229
Feller — Lindeberg      56 17
Feller — Lindeberg condition      56 17
Field      248
Finite probability space      5 115 146 323
Finitely distributed additive function      77 259 260 267 270 275 276 283
Finitely distributed additive function (definition)      258
Finitely monotonic additive function      268 269
Fisher — Courant      163
Fisher — Courant theorem      163 164
Forti and Viola      12 185 186 317
FOURIER      71 74 77 196 199 219 222 223 227 274 327
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)
Fr$\acute{e}$chet — Shohat      59 78
Fr$\acute{e}$chet — Shohat — Wintner      59 60 78
Fubini      68
Functional equation, approximate for $\alpha(x)$      61
Functional equation, Cauchy’s      17 20 76 283 289 179 340
Functions, slowly oscillating      18
Fundamental lemma      80 25 26
Galambos      218 280 281
Gallagher      12 93 185
Gauss      7 57 94 19 329
Gaussian component      51 94
Geometry, Plane Projective      12
Gershgorin      765 376
Gershgorin discs      165 316
Gnedenko      53 55 56 124
Gnedenko and Kolmogorov      24 26 25 29 49 50 57 53 54 55 56 57 17 125 167 201
Group of substitutions      13 183 209
Group of transformations      13 183 209
H$\ddot{o}$lder      779 786 236 373 329 86 191 214
Haar      63 68
Haar measure      63 68
hadamard      7 29
Hahn — Banach      787
Hal$\acute{a}$sz      70 72 27 77 774 224 225 226 233 252 255 256 286 308 372 377 330 337 83 86 125 209 211 212 222 260 285 286 289 296 297 301 303 311 312
Halberstam      6 30 44 47 50 51 202
Halberstam and Davenport      72 185
Halberstam and Elliott      272
Halberstam and Richert      80 185
Halberstam and Roth      77
Hall      333
Hamel      76
Hamilton      339
Hamilton’s principle      339
Hardy      7 3 702 18 239 248 334
Hardy and Ramanujan      2 3 5 73 74 18 19 43 98 99 102 103 104 290 296 302 303 311
Hardy and Wright      85 89 108 112 778 733 734 224 138 139 170
Hardy — Little wood (Hardy and Littlewood)      2 77 102 254 348 357 358 255
Hardy — Littlewood (circle) method      2 6 9
Hardy — Littlewood tauberian theorem      77 254 348 351 358 255
Hardy — Littlewood tauberian theorem, (statement)      102
Hardy, Littlewood and P$\acute{o}$lya      186
Hardy’s      1921
Hartman      292
Hausdorff      340
Hecke      227
Hecke’s dictum      227
Heilbronn      94 774
Heine — Borel      168
Hengartner and Theodorescu      278
hermite      72 762 766 258
Hermitian form, non-negative definite      258
Hermitian matrix, operator      162
Hermitian operator      12
Hermitian operator, spectral radius      12 162
Highest common divisor of a sequence      295
hilbert      787 785
Hilbert’s inequality      185
Hooley      41 332
Ibragimov and Linnik      78
Ikehara — Wiener      100 707 702
Improper distribution function      25
Independence and divisibility by primes      146 24
Independence in probabilistic number theory      4 146
Independent functions      24
Independent random variables      30
Infinite convolutions      37
Infinitely divisible law      49 145 147 167 168 199 201 204 209 338
Infinitely divisible law, characteristic function according to Kolmogorov      51
Infinitely divisible law, characteristic function according to L$\acute{e}$vy — Khinchine      49 50
Infinitely divisible law, convergence of      53
Infinitesimal, variable      54 147
Ingham      248 249 258 260
Ingham’s review      248 258 260
Inner measure      159
Integral equation, approximate      11 213
Interval, positive bounded      72
Inversion formula      28
jacobi      75 321
Jacobi symbol      321
Jessen and Wintner      46 78 793
Jutila      329
K$\acute{a}$tai      34 37 50 51 120 331 333
Kac      4 5 746 18 22 24 25 26
Kac — Erd$\ddot{o}$s (Kac and Erd$\ddot{o}$s)      4 5 74 746 782 274 12 18 20 24 25 26 262 302
Kac — Erd$\ddot{o}$s theorem      18 262
Kac — Kubilius — Erd$\ddot{o}$s      9 31 48 125
Kac’ lecture, and Erd$\ddot{o}$s      24 25
Kac’ letter      24
Kantorovich and Akilov      787
Karamata      78 77
Kesten      278
Khinchine      55 77 125 167
Khinchine and L$\acute{e}$vy      49 57 135 144
Khinchine — L$\acute{e}$vy representation      49 50 57 144
Kobayashi      72 785
Kolmogorov      3 32 44 45 57 52 53 56 77 277 13 17 24 27 37 205
Kolmogorov and Gnedenko      24 26 28 29 49 50 57 53 54 55 56 57 17 125 167 201
Kolmogorov’s inequality      44
Korevaar, van Aardenne — Ehrenfest and de Bruijn      78 77
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