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                    | Apostol T.M. — Introduction to Analytic Number Theory |  
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                    | Предметный указатель |  
                    | | 0, big oh notation      53 Abel, Niels Henrik      77
 Abelian group      129
 Abel’s identity      77
 Abscissa of absolute convergence      225
 Abscissa of convergence      233
 Additive number theory      304
 Algorithm, division      19
 Algorithm, division, Euclidean      20
 Analytic continuation, of Dirichlet L-functions      255
 Analytic continuation, of Dirichlet L-functions of Hurwitz zeta function      254
 Analytic continuation, of Dirichlet L-functions of Riemann zeta function      255
 Apostol, Tom M.      329
 Arithmetic, fundamental theorem of      17
 Arithmetical function      24
 Asymptotic equality      53
 Average (arithmetic mean) of an arithmetical function      52
 Average order      52
 Ayoub, Raymond G.      329
 Bell series      43
 Bell, Eric Temple      29 42 329
 Bernoulli, numbers      265
 Bernoulli, numbers, periodic functions      267
 Bernoulli, numbers, polynomials      264
 Binomial congruence      214
 Borozdkin, K. G.      10 329
 Buhstab, A. A.      11 329
 Cauchy product      44
 Cauchy, Augustin-Louis      44 144 198
 Chandrasekharan, Komaravolu      329
 Character, Dirichlet      138
 Character, Dirichlet, of an abelian group      133
 Character, Dirichlet, primitive      168
 Character, Dirichlet, principal      138
 Chebyshev function
  75 Chebyshev function
  75 Chebyshev, Pafnuti Liwowich      9 75
 Chen, Jing-run      11 304 329
 Chinese remainder theorem      117
 Clarkson, James A.      18 330
 Classes of residues      109
 Clausen, Thomas      275
 Common divisor      14
 Commutative group      129
 Complete residue system      110
 Completely multiplicative function      33
 Conductor of a character      171
 Congruence      106
 Convolution, Dirichlet      29
 Convolution, Dirichlet, generalized      39
 Critical line      293
 Critical strip      293
 Cross-classification principle      123
 Cyclic group      131
 Darling, H. B. C      324
 Davenport, Harold      330
 Decomposition property of reduced residue systems      125
 Derivative of arithmetical functions      45
 Dickson, Leonard Eugene      12 330
 Diophantine equation      5 190
 Dirichlet, character
  138 Dirichlet, character
  , convolution (product)      29 Dirichlet, character
  , divisor problem      59 Dirichlet, character
  , estimate for d(n)      53 57 Dirichlet, character
  , inverse      30 Dirichlet, character
  , L-function      224 Dirichlet, character
  , series      224 Dirichlet, character
  , theorem on primes in arithmetic progressions      7 146 154 Dirichlet, Peter Gustav Lejeune      5 7 29 53 138 146 224
 Disquisitiones Arithmeticae      5
 Divisibility      14
 Division algorithm      19
 Divisor      14
 Divisor function
  38 Edwards, H. M.      330
 Elementary proof of prime number theorem      9 98
 Ellison, W. J.      306 330
 Erdos, Paul      9 330
 Euclidean algorithm      20
 Euclid’s lemma      16
 Euler product      230
 Euler totient function
  25 Euler — Fermat theorem      113
 Euler's summation formula      54
 Euler, Leonhard      4 5 7 9 19 25 53 54 113 180 185 230 308 312 315
 Euler’s constant      53 250
 Euler’s criterion      180
 Euler’s pentagonal-number theorem      312
 Evaluation of
  181 Evaluation of
  181 Evaluation of
  268 Evaluation of
  264 Evaluation of
  266 Exponent of a modulo m      204
 Exponential congruence      215
 Factor      14
 Fermat      7
 Fermat conjecture      11
 Fermat prime      7
 Fermat theorem (little)      114
 Fermat, infinitude of      16 19
 Fermat, Mersenne      4
 Fermat, Pierre de      5 7 11 113 114
 Finite Fourier expansion      160
 Formal power series      41
 Fourier coefficient      160
 Franklin, Fabian      313 330
 Function,
  8 74 Function,
  278 Function, arithmetical      24
 Function, Bernoulli periodic
  267 Function, Chebyshev
  75 Function, Chebyshev
  75 Function, completely multiplicative      33
 Function, Dirichlet
  224 Function, divisor
  ,  38 Function, Euler totient
  25 Function, Hurwitz zeta
  249 Function, k(n)      247
 Function, Liouville
  37 Function, M(x)      91
 Function, Mangoldt
  32 Function, Mobius
  24 Function, periodic zeta F(x, s)      257
 Function, Riemann zeta
  9 249 Function, v(n)      247
 Functional equation for
  263 Functional equation for
  259 Functional equation for
  261 Functional equation, for
  250 Fundamental Theorem of Arithmetic      17
 Gamma function      250
 Gauss sum, associated with
  165 Gauss sum, associated with
  , quadratic      177 306 Gauss, Carl Friedrich      5 7 8 106 165 177 182 185 306 326
 Gauss’ Lemma      182
 Gauss’ triangular-number theorem      326
 Generating function      308
 Geometric sum      157 158
 Gerstenhaber, Murray      186 330
 Goldbach conjecture      9 304
 Goldbach, C      6 9 304
 Greatest common divisor      15 20 21
 Greatest integer symbol      8 25 54 72
 Grosswald, Emil      330
 Group character      133
 Group, abelian      129
 Group, cyclic      131
 Group, definition of      129
 Hadamard, Jacques      9 74 330
 
 | Hagis, Peter, Jr.      5 330 Half-plane, of absolute convergence      225
 Half-plane, of convergence      233
 Hardy, Godfrey Harold      59 293 305 330
 Hemer, Ove      330
 Hilbert, David      293
 Hurwitz formula for
  257 Hurwitz zeta function
  249 251 253 255 Hurwitz, Adolf      249
 Identity element      30 129
 Identity function I(n)      30
 INDEX      213
 Index calculus      214
 Indices (table of)      216 217
 Induced modulus      167
 Induction, Principle of      13
 Inequalities for
  1 272 Inequalities for
  270 287 291 Inequalities for
  270 Inequalities for
  82 Inequalities for
  298 Inequalities for d(n)      294
 Inequalities for nth prime
  84 Inequalities for p(n)      316 318
 Infinitude of primes      16 19
 Ingham, A. E.      330
 Inverse, Dirichlet      30
 Inverse, Dirichlet, of completely multiplicative function      36
 Inversion formula, Mobius      32
 Inversion formula, Mobius, generalized      40
 Iseki, Kaneshiro      99 332
 Jacobi symbol
  188 Jacobi triple product identity      319
 Jacobi, Carl Gustav Jacob      187 305 313 319
 Jordan totient
  48 Kloosterman sum      176
 Kloosterman, H. D.      176
 Kolberg, Oddmund      324
 Kolesnik, G. A.      59
 Kruyswijk, D.      324 327 331
 L-function
  224 Lagrange interpolation formula      158
 Lagrange, Joseph Louis      5 115 144 158
 Lagrange’s theorem on polynomial congruences      115
 Landau, Edmund      59 237 248 301 331
 Landau’s theorem      237 248
 Lattice points      57 62
 Lattice points, visibility of      62
 Law of quadratic reciprocity      185 189 193 200
 Least common multiple      22
 Leech, John      10 331
 Legendre symbol
  179 Legendre, Adrien-Marie      5 67 179 185 331
 Legendre’s identity      67
 Lehmer, Derrick Henry      6 293 316 331
 Lehmer, Derrick Norman      6 331
 Lemma of Gauss      182
 LeVeque, William Judson      2 191 331
 Levinson, Norman      293 331
 Linear congruence      111 112 114 214
 Liouville function
  37 Liouville, Joseph      37
 Little Fermat theorem      114
 Littlewood, John Edensor      10 305 331
 Logarithmic integral Li(x)      102
 Lucas, Edouard      275
 MacMahon, Percy A.      316
 Mean value formulas for Dirichlet series      240
 Mersenne numbers      4
 Mersenne, P.      4
 Mertens, Franz      91
 Mertens’ conjecture      91
 Mills, W. H.      8 331
 Mobius function
  24 Mobius function
  of order k      50 Mobius inversion formula      32
 Mobius inversion formula, generalized      40
 Mobius inversion formula, product form      47
 Mobius, Augustus Ferdinand      24
 Mordell, Louis Joel      305 306
 Multiplication, Dirichlet      29
 Multiplication, Dirichlet of residue classes      138
 Multiplicative function      33
 Multiplicative number theory      304
 Nevanlinna, Veikko      331
 Niven, Ivan      331
 Nonresidue      178
 Number-theoretic function      24
 o, little oh notation      94
 Order of a group      130
 Orthogonality relation for Dirichlet characters      140
 Orthogonality relation, for group characters      137
 Partition      304
 Partition function p(n)      307
 Pentagonal numbers      2 5 311
 Pentagonal-number theorem      312
 Perfect numbers      4
 Periodic arithmetical function      157
 Periodic zeta function      257
 Polya inequality for character sums      173 176 299
 Polygonal numbers      2 5
 Polynomial congruence      115
 Prachar, Karl      331
 Prime number theorem      9 65 74 79 92 94 98 278 289
 PRIMES      2 16
 Primes in arithmetic progressions      7 146 154
 Primes, contained in a factorial      67
 Primitive character      168
 Primitive root      204
 Principal character      134 138
 Product of Dirichlet series      228
 Product, of arithmetical functions      29
 Pythagorean triple      2
 Quadratic, congruence      178
 Quadratic, Gauss sum      177 195
 Quadratic, nonresidue      178
 Quadratic, reciprocity law      185 189 193 200
 Quadratic, residue      178
 Rademacher, Hans      316 331
 Ramanujan partition identities      324 328
 Ramanujan sum      160 176
 Ramanujan, Srinivasa      160 305 324 328
 Reciprocity law for Legendre symbols      185 193 200
 Reciprocity law for quadratic Gauss sums      200
 Reciprocity law, for Jacobi symbols      189
 Reduced fraction      21
 Relatively prime      15 21
 Relatively prime in pairs      21
 Renyi, Alfred      10 332
 Residue class      109
 Residue system, complete      110
 Residue system, reduced      113 125
 Residue, quadratic      178
 Riemann hypothesis      293 301
 Riemann zeta function      249
 Riemann — Lebesgue lemma      279
 Riemann — Stieltjes integral      77
 Riemann, Georg Friedrich Bernhard      9 225 293 332
 Ring of formal power series      42
 Robinson, Raphael M.      7 332
 Rosser, J. Barkley      293 332
 Schnirelmann, L.      10 332
 Selberg asymptotic formula      100 103 104
 Selberg identity      46
 Selberg, Atle      9 46 100 332
 Separable Gauss sums      165 171
 Shanks, Daniel      312 326 332
 Shapiro, Harold N.      85 146 332
 Shapiro’s Tauberian theorem      85
 Shen, Mok-Kong      9 332
 
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