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| Murty M.R. — Problems in analytic number theory |
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| Предметный указатель |
Abscissa of convergence 31 232
Algebraic closure 155
Analytic continuation 74 115 310
Average order 9 188
Bernoulli, function 20
Bernoulli, number 20 33 122 165 243
Bernoulli, polynomial 20 81 123 165 245 322
Bertrand’s postulate 38
Big ‘O’ notation 9
Binomial inversion formula 161 435
Bojanic 160
Bounded variation 274
Cauchy - Riemann equations 260
Cauchy, principal value 54 56 281
Cauchy, sequence 148 150 424
Cauchy, theorem 55 63 289
CHARACTER 22
Character, Dirichlet 26 75
Character, nonprincipal 75
Character, primitive 75 76 80 319
Character, real 228
Character, trivial 23
chebyshev 36 37 38 247
Chebyshev, estimate 266 272 362
Chebyshev, theorem 36 271
Clausen and von Staudt 167 441
Counting zeros 101
De La Vallee Poussin 35 39
Diagonalization 407
Dirichlet 17 27
Dirichlet, character 26 75 219
Dirichlet, divisor problem 27
Dirichlet, hyperbola method 27 28 225 227 229 235 236 294 295
Dirichlet, L-functions 76
Dirichlet, series 7 19 25 31 32 39 43 53 115 221 297 301
Dirichlet, Theorem 17 24 29
Dual 18 407
Duplication formula 334
Equivalent metrics 148
Eraos 39
Eratosthenes - Legendre 127
Euler’s, constant 19 28 92 126 232 344
Euler’s, pioduct 115
Euler’s, theorem 22
Explicit formulas 101 104 369
Explicit formulas, Weil’s 107 109
Fejer kernel 42
Finite order 85
Formula, Euier - Maclaunn summation 20 21 57 285
Formula, Legendre’s duplication 118
Formula, Moebius inversion 4
Fourier, coefficients 69
Fourier, inversion 42 70
Fourier, series 69
Fourier, transforms 42 44 70
Function 71
Function,  71
Function,  327
Function, additive 3
Function, additive, additive 3
Function, additive, completely 3
Function, additive, multiplicative 3 23 48 216 264
Function, arithmetic 3
Function, Beta 91 335
Function, completely additive 3
Function, entire 83 85 88 332
Function, Euler’s 134
Function, Euler’s totient 4
Function, Gamma 91
Function, Jordan’s totient 11 193
Function, Liouville 6 8 65 167 291
Function, Moebius 4 138 173
Function, multiplicative 3
Function, multiplicative, completely 3
Function, primitive 121 378
Function, rapidly decreasing 42
Function, von Mangoidt 4 37 107
Functional, equations 69 72 107 115 303 339 369
Functional, part 231
Gauss 35
Gauss, sums 75 77 122 382
Group of characters 219
hadamard 35 39 340
Hadamard, factorization 92 94 340 344
Hadamard, products 85
Harmonic series 25
Haseigrove 33 244
Ikehara 35
Inclusion - exclusion pxinciple 402
Infinite products 93 188
Integral test 273
Klein four-group 23
Koblitz 164 167
Kubota 167
Kummer 167 440
Kummer, congruences 167 440
Lagrange multipliers 139
legendre 35 127
Legendre, duplication formula 91 380
Legendre, symbol 325
Lemma, Conrey and Ghosh 119
Lemma, Hensel’s 154 155 428
| Lemma, Hensel’s polynomial form of 157 429
Leopoldt 167
Lindeloef hypothesis 289
Little ‘o’ notation 9
Logarithmic integral 35
Maximal ideal 424
Maximum Modulus Principle 117 377
Mazur 166
Measure 164
Methods of contour integration 53
Methods, Lagrange multiplier 408
Moebius, dual 13
Moebius, inversion formula 4 171 175 180 396
Murty, K. 39 260
Nair 37 249
Norm 147
Norm, non — Archimedean 157
Ostrowski 148
P-adic, analytic number theory 152
p-adic, distribution 164
P-adic, gamma function 160
p-adic, integers 152
p-adic, interpolation 158
P-adic, methods 147
p-adic, series 153
P-adic, zeta function 164
Parseval’s formula 42 44
Partial summation 18 129 228 252
Perron’s formula 67 301
Poisson’s summation formula 69 71 76 306
Polya 33 244
Polya - Vinogradov inequality 80 319
Polynomial, Bernoulli 20 33 81
Polynomial, cyclotomic 14
Polynomial, Dirichlet 119
Polynomial, irreducible 201
Primitive, element 121
Primitive, function 121
Primitive, root 23 217 371
Product formula 154 427
Quadratic, nonresidue 373
Quadratic, reciprocity 83 328
Ramanujan 38 184
Ramanujan, hypothesis 116
Ramanujan, identity 185 241
Ramanujan, sum 7 179 206 372
Ramanujan, zeta function 116
Rankin’s trick 130 135 398
Riemann — Lebesgue lemma 42 44
Riemann — Lebesgue lemma, rigid analytic spaces 155
Riemann, generalized 373
Riemann, hypothesis 62 64 101 112 243 365
Riemann, sums 165
Riemann, zeta function 72
Schwartz space 42
Selberg 39
Selberg, class 107 115
Selberg, conjectures 123 125
Selberg, identity 49 267
Siegel zero 97
Sieve, Brun’s 131 404
Sieve, Brun’s elementary 133 137
Sieve, methods 127
Sieve, methods of Eratosthenes 127 132 135 397 402
Sieve, Selberg’s 138 140 416
Simple zeros 78
Stieltjes integral 20
Stirling’s formula 92 337 341
Strong multiplicity 124
Summation techniques 17
Symmetric difference 126
Theorem, Brun — Titchmarsh 143 412
Theorem, Cauchy’s 55 63
Theorem, Chebyshev’s 415
Theorem, Chinese remainder 23 416
Theorem, Dirichlet’s 17 24 29
Theorem, Euler’s 22
Theorem, Fejer’s 69
Theorem, Fermat’s little 441
Theorem, Fubini’s 334
Theorem, Hadamard factorization 340
Theorem, Ikehara — Wiener 42 46
Theorem, Jensen’s 85 87 327
Theorem, Landau’s 32 239
Theorem, Landau’s for integrals 32 243
Theorem, Mahler’s 159 161 162
Theorem, Mahler’s interpolation 160
Theorem, Mazur 167
Theorem, Mertens 128 130 398
Theorem, Ostrowski 147 149
Theorem, Phragnren — Lindelof 116 117
Theorem, prime number 35 46 57 59 276
Theorem, Selberg 118 120
Theorem, Tauberian 300
Theorem, unique factorization 176 419
Theorem, Wilson’s 159 168 431 443
Titchmarsh divisor problem 143 413
Triangle inequality 147
Trigonometric identities 40
Washington 167
Wiener 35
Zero-free regions 94 96
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