Murty M.R. — Problems in Analytic Number Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Murty M.R. — Problems in Analytic Number Theory

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Название: Problems in Analytic Number Theory

Автор: Murty M.R.

Аннотация:

This book gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic methods and the ways in which they are used to study the distribution of prime numbers. The book also includes an introduction to p-adic analytic methods. It is ideal for a first course in analytic number theory. The new edition has been completely rewritten, errors have been corrected, and there is a new chapter on the arithmetic progression of primes.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2007

Количество страниц: 528

Добавлена в каталог: 13.05.2008

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Предметный указатель

Abscissa of convergence      31 265
Additive function      3
Analytic continuation      72 115 280
Archimdean valuation      148
Arithmetical functions      3 212
Asymptotic distribution function      180 484
Average order      10 215
Bernoulli distribution      165
Bernoulli number      20 33 122 240 407
Bernoulli polynomial      20 33 81 123 165 270 348 410
Bertrand’s postulate      38
beta function      91
Beurling, A.      183
Big O notation      9
Binomial inversion formula      161 459
Bojanic, R.      161
Brun sieve      131
Brun — Titchmarsh theorem      144 438
Brun, V.      136
Brun’s elementary sieve      133 137 429
Brun’s theorem      431
Champerowne’s number      180
Characters      22 237
Chebotarev density theorem      191
Chebyshev, P.      36
Chebyshev’s theorem      36 273 417
Clausen and von Staudt theorem      168 467
Completely additive      3
Completely multiplicative      3
Completely multiplicative function      242
Conrey, B.      118
Copeland      180
Counting zeros      101 118 385
Cyclotomic polynomial      14 231
de La Vallee Poussin, C.      35 39
Dirichlet character      25
Dirichlet L-functions      76 335
Dirichlet series      19 39 53 115
Dirichlet’s Theorem      17 24 29 246
Discrepancy      182 485
Divisor function      3 212 238
Duplication formula      351
Elliptic curves      192
Equidistribution      189 475 488
Equivalent metrics      148
Erdos — Turan theorem      188 488
Erdos, P.      39 180
Euler product      116
Euler — Maclaurin sum formula      311
Euler’s constant      19 259
Euler’s function      4 219
Explicit formulas      101 104 385
Fejer, L.      69 193
Fibonacci number      174 480
Finite order      85
Formal Dirichlet series      7 208
Fourier inversion formula      70
Fourier transform      42
Functional equation      69 83 115 329 406
Gamma function      91
gamma, function      358
Gauss sums      75 333
Generalized Riemann hypothesis      112 397
Generalized Wiener — Schoenberg criterion      195 496
Ghosh, A.      118
Haar measure      189
Hadamard factorization      88 92 366
Hadamard products      85 357
Hadamard, J.      35 39
Haselgrove, C.      33
Hecke eigenform      192
Hensel’s Lemma      155 157 454
Hyperbola method      27 251 255 264 320
Ikehara — Wiener theorem      288
Imprimitive character      75
Irreducible polynomial      13 226
Jensen’s theorem      85 87 357
Jordan’s totient function      11 219
Kummer congruences      167
Kummer, E.      168 466
Lagrange multipliers      139
Landau’s theorem      32 268 420
Langlands program      192
Lebesgue dominated convergence theorem      181
Legendre’s duplication formula      91 118 351
Lindelof hypothesis      64 315
Liouville function      8 205 317

Little o notation      9
Liuville function      33
Logarithmic integral      35
Mahler, K.      163
Mahler’s interpolation theorem      161
Maximum modulus, principle      116 403
Mazur measure      166
Mazur, B.      167
Mean Value Theorem for Integrals      342
Mertens theorem      128
Method of contour integration      53 305
Mobius function      4 199
Mobius inversion      4
Mobius inversion formula      13 199
Montgomery, H.      183 188
Mordell, L.      191
Multiplicative function      3
Murty, K.      41
Nair, M.      37
Norm      147
Normal numbers      177 483
Order of a function      85
Ostrowski’s theorem      147 449
p-adic distribution      165
p-adic gamma function      160
p-adic interpolation      159 456
p-adic zeta function      165 463
Partial summation      17
Perron’s formula      67 327
Peter — Weyl theorem      190
Phragmen — Lindelof theorem      116 403
Poisson summation formula      69 71 329
Polya conjecture      33
Polya — Vinogradov inequality      80 345 400
Prime number theorem      35 47 57 60 273 311
Primes in arithmetic porgressions      237
Primitive character      75 122
Primitive function      121 123 411
Primitive root      23 243
Product formula      155 453
Quadratic reciprocity      81 83 355
Ramanujan $\tau$ -function      191
Ramanujan hypothesis      116
Ramanujan identity      267
Ramanujan sum      7
Ramanujan sums      206
Ramanujan, S.      9 38 210
Rankin’s trick      424
Riemann hypothesis      62 101 106 194 393 494
Riemann zeta function      19 72 332
Riesz representation theorem      181
Sato — Tate conjecture      191
Schoenberg      181
Schwartz space      42
Selberg class      107 115 403
Selberg identity      50
Selberg, A.      39 120 183 185
Selberg’s conjectures      123 411 416
Selberg’s identity      296
Selberg’s sieve      432
Selberg’s siever      138
Serre, J.-P.      189 191 489
Set asymptotic distribution function      194
Set equidistributed      194 494
Siegel zero      98
Sieve methods      127 423
Sieve of Eratosthenes      127 132 423 428
Simply normal      177
Stirling’s formula      92 368
Strong multiplicity one      124
Summation techniques      17
Tauberian theorem      43 489
Taylor, R.      192
Titchmarsh divisor problem      144 439
Uniform distribution      171 475
Valuation      148
van der Corput’s theorem      174
von Mangoldt function      4
Weierstrass approximation theorem      172
Weil’s explicit formula      107 109
Weyl criterion      172 183 478
Weyl criterion for compact groups      190
Wiener      181
Wiener — Ikehara theorem      35 42 288
Wiener — Schoenberg theorem      181 485
Wilson’s Theorem      469
Zero-free region      94 374

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