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Elliot P.D.T.A. Ч Probabilistic Number Theory One
Elliot P.D.T.A. Ч Probabilistic Number Theory One

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Ќазвание: Probabilistic Number Theory One

јвтор: Elliot P.D.T.A.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1979

 оличество страниц: 393

ƒобавлена в каталог: 13.09.2007

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\mathrm{L}^2$-norm      12 23
Abel      352
Abundant numbers      3Ч4 189
Aczel      76
Additive function, finitely distributed      258 259 260 267 270 275 276 283
Additive function, finitely distributed (definition)      11
Adjoint of operator      181Ч182
Akilov and Kantorovich      181
Algebra of sets      29Ч30 115Ч146
Analytic characteristic functions      57 112Ч113
Asymptotic density      295 297;
asymptotic relations      19Ч21
Bakstys      280
Banach Ч 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 Ч Esseen      74 101 117 217
Berry Ч Esseen theorem      74 117
Bertrand      3
Bessel Ч Hagen      3 4 189
Billingsley      30
Birch      14
Bombieri      12 90 92 93 184 185 186 317
Bombieri and Davenport      185
Borel      3
Borel Ч Cantelli      45 46
Borel Ч Cantelli lemma, applications      45Ч46
Borel Ч Caratheodory      58
Borel Ч Caratheodory lemma      58
Brownian motion      3
Brun      4 9 80 134 184 210 213
Brun Ч Titchmarsh      90 120 135 160 161 213
Brun's sieve      4 9 80 129
Burgess      154 157
Cantelli Ч Borel      45 46
Caratheodory Ч Borel      58
Cartwright      94
Cauchy      7 14 17 20 46 76 231 239 283 289 290 329
Cauchy law      14
Cauchy Ч 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      110Ч111
Character, Dirichlet, primitive      110
Characteristic function      27
Characteristic function (definition)      9
Characteristic function, analytic      57 112Ч113
Characteristic function, component of      113Ч114
Characteristic function, convergence of      28
Chowla, S.      4 189
Circle method      2 6Ч9
Class Number, quadratic      14 110Ч111 117
Classification      13
Coefficients, Fourier      66
Compactness lemma      25
Component of characteristic function      113Ч114
Component of distribution function      113
Concentration function      31 217Ч218
Conditional probability      31 35
conjugate      12 181Ч182
Continuity criterion, Levy's      46 78
Continuity of distribution function      48Ч49
Control, mathematical      13
Convergence, characteristic functions      28
Convergence, Fourier coefficients      67Ч68
Convergence, Mellin Ч Stieltjes transforms      63
Convergence, modified-weak      273Ч274 280
Convergence, modified-weak (definition)      63
Convergence, weak      24Ч30
Convolution      30 254Ч255
Convolutions, infinite      37
Courant Ч Fisher      163
Courant Ч Fisher theorem      163Ч164
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 Ч 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 ФNotationФ
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      111Ч112
Dirichlet, multiplication, convolution      98 109
Discriminant of quadratic field      110Ч111
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      48Ч49
Distribution functions (mod 1)      65
Distribution functions (mod 1) convergence      65Ч68
Distribution functions (mod 1) discontinuous, quantitative Fourier inversion      75Ч76
Distribution functions (mod 1), continuity of      67
Distribution law      24
Doeblin      217
Dual      12 13
Dual of operator      12 181Ч182
Dual of Turan Ч Kubilius inequality      13 147Ч186 194 335
Dual space      181Ч182
Duality principle      150 162 185Ч186 316Ч317
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 Ч Kac Ч Kubilius      9
Erdos Ч Wintner theorem      187Ч224
Erdos' sample paper      207Ч210
Erdos' sample paper, commentary on      210Ч213
Esseen      74 78 203 218
Esseen Ч Berry      74 101 117 217
Esseen Ч 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      188Ч189 213 214
Fainleib      74 75 203 219
Fainleib and Levin      11 286
Fejer      3 70 78 101 229
Fejer kernel      78 101 229
Feller Ч Lindeberg      56
Feller Ч Lindeberg condition      56
Finite probability space      5 115Ч146
Finitely distributed additive function      258 259 260 267 270 275 276 283
Finitely distributed additive function (definition)      11
Finitely monotonic additive function      268Ч269
Fisher Ч Courant      163
Fisher Ч Courant theorem      163Ч164
Forti and Viola      12 185 186 317
Fourier coefficients      66
Fourier inversion (mod 1), quantitative      74Ч76
Fourier inversion, quantitative      69
Fourier Ч Stieltjes      61 305
Fourier Ч Stieltjes transform      61; see also УCharacteristic FunctionФ
Frechet Ч Shohat      59 78
Frechet Ч Shohat Ч Wintner      59Ч60 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 Ч 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 Ч Littlewood (Hardy and Littlewood)      2 77 102 254 348 351 358
Hardy Ч Littlewood circle method      2 6Ч9
Hardy Ч Littlewood tauberian theorem      102 254 348 351 358
Hardy Ч 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 Ч 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 Ч Khinchine      49Ч50
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 Ч Erdoes (Kac and Erdos)      4 5 14 146 182 214
Kac Ч Kubilius Ч Erdos      9
Kantorovich and Akilov      181
Karamata      18 77
Kesten      218
Khinchine      55 77
Khinchine and Levy      49 57
Khinchine Ч Levy representation      49Ч50 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      110Ч111
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 Ч Erdoes Ч Kac      9
Kubilius Ч Tunin inequality      6 13 147Ч186 192 199
Kubilius Ч Tunin inequality dual of      13 147Ч186 194 335
Kubilius Ч Turan      6 13 147 152 158 173 182 185 192 199 218
Kubilius' model      115Ч146
Kubilius' model, construction of      119
Kuipers and Niederreiter      78
Kummer      111
L-series, Dirichlet      14 110Ч111 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 183Ч186 317
Law, Cauchy      14
Law, normal      52
Law, normal (definition)      11
Law, Poisson      52Ч53
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 $\mathrm{L}^2$-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 Ч Khinchine representation      49Ч50 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 Ч Feller      56
Lindeberg Ч Feller condition      56
Linnik      8 9 58 78 93 112 113 183 184 218 317
Linnik and Ibragimov      78
Littlewood and Offord      217
Littlewood Ч 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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