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| Knopfmacher J. — Abstract Analytic Number Theory |
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| Предметный указатель |
 -formula 47
-formula, finite, or generalized 47
 power 45
power, multiplication 185
power, quotient 102
(t)-adic topology for C[[t]] 35
Abelian groups (finite), category of 17
Absolute formation structure over 268
Absolute ideal class formation 254
Abstract prime number theorem, additive 239
Abstract prime number theorem, for formations 278
Abstract prime number theorem, subject to Axiom A 154
Additive arithmetical category 56
Additive arithmetical semigroup 56
Additive function 33
Algebraic integers, ring of 14
Algebraic number field 14
Almost all elements of arithmetical semigroup 177
Almost even compactification 192
Almost even function,  or (B) 207
Almost even function, uniformly 189
Almost periodic function, arithmetical 215
Almost periodic function, of a real variable 148
Approximate,  moment 100
Approximate, (relative) density 90
Approximate, average value 90
Arithmetical category 16
Arithmetical formation 251
Arithmetical function 23
Arithmetical morphism 22
Arithmetical progression 252
Arithmetical progression (generalized) 253
Arithmetical semigroup 11
Arithmetically equivalent 22
Associate class 12
Asymptotic moment 100
Asymptotic (relative) density 90
Asymptotic distribution function 145
Asymptotic frequency 149
Asymptotic mean-value 90
Average, order 111
Average, value (approximate) 90
Axiom  264
Axiom  278
Axiom A 75
Axiom C 220
Character, group (of formation) 257
Character, of a formation 257
Character, residue class (mod m) 257
Characteristic function of distribution function 145
Characteristic function of k-free elements 40
Characteristic function of subset 90
Class group of formation 251
Class number, of algebraic number field 254
Class number, of formation 251
Compactification, almost even 192
Completely, additive 33
Completely, multiplicative 33
Congruence in integral domain 252
Convolution of arithmetical functions 23
Coprime 112
Core 46
Cyclotomic, integer 49
Cyclotomic, polynomial 49
Cyclotomic, rational 49
Dedekind zeta function 62
Degree mapping, on arithmetical semigroup 56
Density, approximate (relative) 90 112
Density, asymptotic (relative) 90 112
Derivative (formal) 32 61
Dirichlet's formula, for divisor function 92 101
Dirichlet, algebra 23
Dirichlet, L-series 261
Dirichlet, series (formal) 24
Dirichlet, series (ordinary) 79
Distribution function 143
Distribution function, asymptotic 145
Divisor 25
Divisor function 39
Divisor function, generalized 39
Divisor function, unitary 39
Divisor, unitary 39
Divisor-sum function 108
Double series (product) of arithmetical functions 30 32
Enumerating, function 55
Enumerating, power series 58
Euclidean Domain 12
Euler, constant 89
Euler, constant of a class 271
Euler, function 40
Euler, product formula (analytical) 79 80 84 225 270
Euler, product formula (classical) 59
Euler, product formula (formal) 36 56—8 224 261
Euler-type function 108
Even arithmetical function 187 189
Formal derivative 32 61
Formal Dirichlet series 24
Formal Euler product formula 36 56—8 224 261
Formal power series 35
Formation, arithmetical 251
Fourier, coefficient of arithmetical function 197 204
Fourier, transform of even function 197
frequency 149
Frequency, asymptotic 149
Galois polynomial ring 60
Gamma function 227
Gaussian integers 13
Generalized arithmetical progression 253
Generalized Dirichlet algebra 54
Generalized divisor function 39
Generalized ideal class 251
Generalized partition functions 64 68
Generalized progression (in integral domain) 253
Generating function 58
Greatest common divisor 33 112
Greatest square-free divisor 46
Grothendieck group 22
Group of fractions 22
| Hecke — Landau L-series 262
Holder's relation 196
Hurwitz zeta function 264
Ideal class 254
Ideal class, formation (absolute) 254
Ideal class, generalized 251
Ideal class, group (absolute) 254
Ideals, in algebraic number field 14
Ikehara's theorem 157
Indicator, of arithmetical function 134
Indicator, of category 138
Indicator, of number field 140
Irreducible polynomials over GF(tf) 60
k-associated function 197
K-free element 40
L-series, Dirichlet 261
L-series, Hecke — Landau 262
L-series, of formation 261 270
Landau's formula 168
Landau's prime ideal theorem 15
Landau's relative prime ideal theorem 278
Lie algebras (semisimple finite-dimensional), category of 18
Lie groups (compact simply-connected), category of 19
Liouville function 40
Logarithmic, derivative 61
Logarithmic, integral 162
Logarithmic, maximum order of magnitude 134
Maximum order of magnitude 133
Maximum order of magnitude, logarithmic 134
Mean-value, asymptotic 90
Mean-value, upper 206
Mertens's formula 171
Minimum order of magnitude 133
Mobius, functions 36
Mobius, inversion principle 38
Modules (finite), category of 20
Moment, approximate  100
Moment, asymptotic 100
Multiplicative function 33
Norm on arithmetical semigroup 11
Norm on Dir(G) 24
Normal order of arithmetical function 180
Normalization principle 78
Order of arithmetical function 24
Order of magnitude 133—4
Order of power series 35
Orthogonality lemma for formations 260
p-groups (finite abelian), category of 63
P-modules (finite)
P-modules (finite), category of 67
P-rings (semisimple finite), category of 64
Parseval identity for  205
Parseval identity for  198
Partial summation 82
Partition function, classical 63
Partition function, generalized 64 68
Partition function, weighted 228
PIM-function 36
Plancherel's theorem for 35 198
Point-wise
Prime number theorem, abstract (for formations) 278
Prime number theorem, abstract (subject to Axiom A) 154
Prime number theorem, additive (abstract) 239
Prime number theorem, classical 1 12
Prime number theorem, for arithmetical progressions 251
Prime, element of integral domain 12
Prime, ideal of number field 14
Prime, ideal theorem 15
Prime, of arithmetical semigroup 11
Prime, of category 16
Prime-divisor functions 39
Prime-independent function 33
Pseudo-convergent, double product 32
Pseudo-convergent, double series 30
Pseudo-convergent, product 28
Pseudo-convergent, series 26
Pseudo-metrizable spaces (finite), category of 20
Ramanujan, coefficients (of arithmetical function) 205
Ramanujan, expansion (of arithmetical function) 197 204
Ramanujan, sums (classical) 213
Ramanujan, sums (in arithmetical semigroup) 185
Relative, density 90
Relative, prime ideal theorem 278
Relative, simple ring theorem 279
Relatively prime 112
Renyi's formula 151
Riemann zeta function 59
Riemannian manifolds (compact symmetric), category of 19
Semisimple algebras (finite-dimensional), category of 18
Semisimple Lie algebras (finite-dimensional), category of 18
Semisimple rings (finite), category of 17
Separable arithmetical function 195
Simple ring theorem, relative 74
Square-free (2-free) element 40
Square-full element 46
Steinitz numbers 213
Substitution endomorphism 41
Symmetric Riemannian manifolds (compact), category of 19
Torsion modules (finitely-generated), category of 20
Transfer principle for formations 265
Uniform norm for bounded, arithmetical functions 189
Uniformly almost even function 189
Unique factorization, domains 12
Unique factorization, for ideals in a number field 14
Unique factorization, in arithmetical semigroup 11
Unique factorization, theorem for principal ideal
Unitary divisor 39
Unitary-divisor function 39
Upper mean-value 206
von Mangoldt function 40
Weak, convergence (of distribution functions) 144
Weak, limit (of distribution functions) 145
Weighted partition function 228
Zeta function of a class 262
Zeta function of arithmetical semigroup 36 57 79
Zeta function of category 57
Zeta function of Dedekind 62
Zeta function of Riemann 59
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