Elliot P.D.T.A. — Probabilistic Number Theory Two: Central Limit Theorems :: Электронная библиотека попечительского совета мехмата МГУ

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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:

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

Предметный указатель

kronecker      770 777 313 319 320
Kronecker symbol      110 111 313
Kronecker symbol, primitive character      110 319
Kubik      336
Kubilius      5 6 77 80 775 779 722 723 725 726 728 729 738 739 740 742 744 745 146 147 748 780 787 258 286 12 15 17 22 23 25 26 28 50 145 263 264 267 287 288 303 331 336
Kubilius — Erd $\ddot{o}$ s — Kac      9 31 48 125
Kubilius — Tur $\acute{a}$ n      6 13 147 152 158 173 182 185 192 199 275 16 29 31 55 113 114 118 266 268 269 272 282
Kubilius — Tur $\acute{a}$ n inequality      6 13 147 192 199 14 29 31 113 118 266 268 269 272 282
Kubilius — Tur $\acute{a}$ n inequality, dual of      13 147 194 335 55 114
Kubilius’ model      115 146
Kubilius’ model, construction of      779 12 26 38 264 267 303
Kuipers and Neiderreiter      78
Kummer      111 329 338
Kummer’s problem and -series      329 338
L$-series, Dirichlet      14 110 111 114 241 313
L$-series, Kummer’s problem      329 338
L $\acute{e}$ vy      3 14 24 25 31 46 50 51 52 53 57 78 193 195 217 219 2 31 36 95 124 135 167 331
L $\acute{e}$ vy and Khinchine      49 57 135 144
L $\acute{e}$ vy metric, distance      14 24 31 33 48 56 95 96 97 132 134
L $\acute{e}$ vy representation, formula      50
L $\acute{e}$ vy representation, modified      51 124
L $\acute{e}$ vy — Khinchine representation      49 50 57 144
L $\acute{e}$ vy’s continuity criterion      46 78
Lagrange      339
Lagrange’s equations      339
Lambert      219 334
Lambert series      219 334
Lambert series, tauberian theorem      334
Landau      1 94 111 254 25 239 261 313 320
Landau and Walfisz      100
Lang      101
Large deviation inequality for random variables      127
Large deviations of additive functions      120 287 288 289
Large sieve      9 10 12 13 93 165 183 317 260 328
Lavrik      329
Law, Cauchy      14 136 143
Law, normal      11 17
Law, Normal, (definition)      52
Law, Normal, Gaussian      19 24 26 136 142 148 262 335
Law, Poisson      52 53 148 172 337
Law, stable      11 134 145
Laws, on a finite interval      58
Laws, which cannot occur      169
Lebesgue      16 19 21 22 23 48 59 67 107 222 228 258 260 359 7 63 74 91 92 152 154 155 164 170 171 199 308 314 327
Lebesgue $L^{2}$ -class      22
legendre      110 154 245 320
Legendre symbol      110 154 245 320
LeVeque      6 75 76 20 22 24 267 286 287
LeVeque’s conjecture      6 20 22 267 286 287
Levin and Falnleib      11 286 145
Levin and Timofeev      10 12 257 258 122 123 125 169 184 185 204 208 209 210
Levin, Barban and Vinogradov      174 27 50
Levin, Timofeev and Tuliaganov      274 275 280 281
Liapounoff      218
Limit law      24
Limiting distribution of a strongly additive function      4
Lindeberg      335
Lindeberg condition      335
Lindeberg — Feller      56 17
Lindeberg — Feller condition      56 17
Linnik      8 9 58 78 93 112 113 183 184 218 317 40
Linnik and Ibragimov      78
Liouville      238 254
Liouville’s function      238 254
Little wood — Hardy (Littlewood and Hardy)      2 77 102 254 348 351 358 255
Littlewood and Offord      217
Littlewood, P $\acute{o}$ lya and Hardy      186
Lo $\grave{e}$ ve      127
Lubell      78
Lukacs      78
M $\ddot{o}$ bius      85 251 254 282 301 212 238
M $\ddot{o}$ bius inversion      85
Major Arcs, intervals      7
Mann      77 293
Mann’s theorem      77 293
Manstavicius      286 305
Marcinkiewicz      58
Marek      111
Matthews      72 185
Mean, of a random variable      30
Measure      16
Measure probability      29 30 115
mellin      61 78 279 307 322
Mellin transform, M-transform      61 141 279 307 94 233 322
Mellin — Stieltjes      61 141
Mellin — Stieltjes transform      61 141 279 307
Mendelssohn, Fanny      111
Mendelssohn, Felix      111
Mendelssohn, Moses      772
Mendelssohn, Rebecka      111 112
Mertens      89 242
Method of Tur $\acute{a}$ n, commentary on      112
Metric, L $\acute{e}$ vy      14 24 31 33 48 56 95 96 97 132 134
Minor Arcs, intervals      7 8 9
Mirsky      762 166
Model for multiplicative functions      140
Models for strongly additive functions      115 146
Modified — L $\acute{e}$ vy representation      51 124 135
Moments, determination by      60 61
Moments, method of      59
Montgomery      93 185 229 235 317 138
Montgomery and Vaughan      185
Mordell      213
Munroe      18
Narkiewicz      103
Natural boundary      100
Niederreiter and Kuipers      78
Norm, $L^{2}$       12 23
Norm, algebraic      114
Norm, operator      181 186
Normal law      11 17
Normal law (definition)      52 24 26 136 142 148 262 335
Normal law (Gaussian)      19
Normal number of prime factors      2
Normal order of an arithmetic function      2 14 41 43 98
Normal order zero      101
Norton      104 288
Offord and Littlewood      277
Operator, adjoint of      181 182
Operator, Dirichlet-series type      186
Operator, dual of      12 181 182
Operator, norm      181 186
Outer measure      159
P $\acute{o}$ lya — Vinogradov      154 316 321 339
P $\acute{o}$ lya — Vinogradov inequality      154 316 321 339
P $\acute{o}$ lya, Hardy and Littlewood      786
Pan      184
Pandora      98
Parseval      8 23 228 235 236 77 219 230 260 307
Parseval’s relation      8 23 228 235 236 77 219 230 260
Partitions      2
Paul      330
Perfect numbers      4
Periodic continued fraction      138
Perron      94 95 322 72 89 195
Perron’s theorem      94 95 322 326
Philipp      727 288
Plancherel      22 23
Plancherel’s identity      23 228 235 236 77 219 230 260
Poincar $\acute{e}$       3
poisson      52 21 145 148 172 173 199 337
Poisson law      52 — 53 148 172 337
Positive interval, bounded      72
Postnikov      77 74 78
Prachar      90 97 92 95 247
Prime ideal theorem      94
Prime number theorem      10 90 145 254 283 238
Prime number theorem, elementary proof      10 90 211 248
Prime numbers in arithmetic progressions      90 92 241
Prime Numbers in Arithmetic Progressions, distribution      89

Primitive root, least positive      158
Probability measure      29 30 115
Probability space      29 115 146
Products of independent random variables      141 142 144
Proper distribution function      25
Purity of type      46 78 292
Quadratic Class Number      14 110 117 313
Quadratic residues, least pair of      153
Quasi-primes      42
R $\acute{e}$ nyi      3 9 72 24 47 92 93 783 784 278 377 17 20 51 294 311
R $\acute{e}$ nyi and Erd $\ddot{o}$ s      333
R $\acute{e}$ nyi and Tur $\acute{a}$ n      6 22 23 286 287
Rado      274
Raikov      58 772 773 172
Ramanujan      7 24
Ramanujan and Hardy      2 3 5 73 74 18 19 43 98 99 102 103 104 290 296 302 303 311
Random variable      29
Random variable, infinitely divisible      49
Relations asymptotic      19 21
Relatively stable      119
Richert and Halberstam      80 185
Riemann      96 97 154 338 341 79 185 193 241 248
Riemann hypothesis      97
Riemann zeta function      96
Riemann zeta function, functional equation      97
Rodosskii      245
Rogozin      32 78 278
rosser      22 24
Roth      72 784
Roth and Halberstam      77
Ruzsa, S $\acute{a}$ rk $\ddot{o}$ zy and Erd $\ddot{o}$ s      290 296
Ryavec      283 289
Ryavec and Elliott      10 257 258 265 268 283 306 169
Ryavec and Erd $\ddot{o}$ s      268
S $\acute{a}$ rk $\ddot{o}$ zy      312
S $\acute{a}$ rk $\ddot{o}$ zy, Erd $\ddot{o}$ s and Ruzsa      290 296
Sathe      23 302
Schmidt, R.      78 77
Schnirelmann      77 292 293 294 296
Schnirelmann density      77 293
Schnirelmann sum      293
Schoenberg (Sch $\ddot{o}$ nberg)      4 789 273 274 24
Schur, J.      274
Schwarz — Cauchy      42 68 735 149 150 151 160 161 164 168 174 196 197 201 202 234 243 246 271 300 304 317 338 339 345 348 349 28 42 43 57 117 220 259 278 283
Schwarz, L.      248
see also Notation Asymptotic density, lower      295 297
see also Parseval’s relation Plancherel’s theory      22
Segal      98
Selberg      79 80 84 119 127 129 142 145 176 182 185 213 23 44 215 248 249 250 252 253 254 255 257 269 287
Selberg and Erd $\ddot{o}$ s      10 256 211 248 258
Selberg and Erd $\ddot{o}$ s, elementary proof of P.N.T.      248 — 253
Selberg’s formula      248 249 250 252 255
Selberg’s sieve method      79 89 120 129 142 145 176 185 213 44 215 269
Shapiro      17 50 335
Shifted primes      9
Shohat — Fr $\acute{e}$ chet      59 78
Siegel — Walfisz      97 315 339
Sierpinski      76
Sieve, Brun      4 9 80 129 21 25 44
Sieve, large      9 10 12 13 93 165 183 317 260 328
Sieve, Selberg      79 — 89 120 129 142 145 176 185 213 44 215 269
Skew — Hermitian form      166
Slowly decreasing functions      102
Slowly oscillating functions      18
Solovay      340
Spectral radius      12 162
Spectral radius, of Hermitian matrix, operator      12 162
Spemer      32 78 274 276 278
Sperner’s lemma      32 78 214 216 218
Stable law      11 134 145
Stable law, characteristic exponent      135 142
Stable law, modified — L $\acute{e}$ vy representation      135
Steinhaus      76 76 267 283 24
Steinig and Diamond      261
Stepanov      755
Stieltjes — Fourier      67 305
Stieltjes — Mellin      67 747
Stirling      34 299 302
Stolz      338
Stone — Weiers trass      307
Substitutions, group of      13 183 209
Sums of independent random variables, limit theorems      54
Surrealistic Continuity Theorem      265 269 291
Sziisz      224
Tauber      77 700 707 702 254 357 358 255 260 334
Tauberian theorem, Hardy and Littlewood      77
Tauberian theorem, Hardy and Littlewood (statement)      102 254 348 351 358 255
Taylor      704 298
Tchebycheff      3 36 44 792 235 18 41 81 241
Tchebycheff’s inequality      3 192 18
Tchudakoff      260
Theodorescu and Hengartner      278
Three Series Theorem, Kolmogorov      37 38 77
Timofeev      285 286
Timofeev and Levin      10 12 257 258 122 123 125 169 184 185 204 208 209 210
Timofeev, Tuliaganov and Levin      274 275 280 281
Titchmarsh      10 22 58 59 70 90 94 95 97
Titchmarsh — Brun      90 120 135 160 161 213 32
Tjan      219
Toleuov and Fa $\breve {\iota}$ nle $\breve {\iota}$ b      46 51
Total event      29
Truncated additive functions      5
Tuliaganov, Timofeev, and Levin      274 275 280 281
Tur $\acute{a}$ n      3 4 5 6 147 180 181 182 185 16 18 20 22 23 24 41 43 50 98 112 118 119 120
Tur $\acute{a}$ n and Erd $\ddot{o}$ s      75
Tur $\acute{a}$ n and R $\acute{e}$ nyi      6 22 23 286 287
Tur $\acute{a}$ n — Kubilius      6 13 147 152 158 173 182 185 192 199 218 16 29 31 55 113 114 118 266 268 269 272 282
Turan and Erdos inequality      75
Turan — Kubilius inequality      6 13 147 192 199 14 29 31 113 118 266 268 269 272 282
Turan — Kubilius inequality, dual of      13 147 194 335 55 114
Turan’s letter      18 20
Turan’s letter, commentary on      20 24
Turan’s method, commentary on      112
TYPE      26
Uniform distribution (mod1)      66 69
Uniform law (mod1)      66
Urbanik      336
Uzdavinis      134 44 45 51 263 268
van Aardenne — Ehrenfest, de Bruijn and Korevaar      18 77
Variance, random variable $\sigma^{2}$ $D^{2}$       30 — 31
Vaughan and Montgomery      185
Vinogradov — Barban — Bombieri      51 269
Vinogradov — P $\acute{o}$ lya      154 316 321 339
Vinogradov — Polya inequality      154 316 321 339
Vinogradov, A.I.      92 93 184 338
Vinogradov, A.I. and Barban      122 126 263
Vinogradov, A.I., Barban and Levin      174 27 50
Vinogradov, I.M.      2 7 8 154 755 41 138 245
Viola and Forti      72 185 186 317
von Mangoldt      97 311 214
von Mangoldt’s function      97 311
Walfisz and Landau      100
Walfisz — Siegel      97 315 339
Weak convergence of distribution functions      24 25
Weak convergence of distribution functions (mod      1 65
Weak convergence of measures      24 30
Weierstrass — Stone      307
Weil      755
Weyl      69 75 284
Weyl’s criterion      69
Weyl’s criterion, quantitative      75
Wiener      68 100
Wiener - Ikehara      100 101
Wiener — Ikehara      100 101 102
Wiener — Ikehara tauberian theorem      100 101
Wintner      3 10 59 78 254 285 24
Wintner and Erd $\ddot{o}$ s      4 10 187 214 254 280 24 172 260 332 335
Wintner and Jessen      46 78 193
Wintner — Erdos theorem      187 224
Wirsing      10 11 90 144 225 226 227 254 255 256 273 331 213 217 218 241 256 257 258 259 260 261

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