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Knopfmacher J. — Abstract Analytic Number Theory
Knopfmacher J. — Abstract Analytic Number Theory

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Название: Abstract Analytic Number Theory

Автор: Knopfmacher J.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1976

Количество страниц: 322

Добавлена в каталог: 23.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$ \zeta$-formula      47
$ \zeta$-formula, finite, or generalized      47
$m^{th}$ power      45
$m^{th}$ power, multiplication      185
$m^{th}$ 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, $(B^{\lambda})$ or (B)      207
Almost even function, uniformly      189
Almost periodic function, arithmetical      215
Almost periodic function, of a real variable      148
Approximate, $k^{th}$ 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 $k^{th}$ 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 $A*$      264
Axiom $A^{**}$      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 $(k^{th})$      100
Moment, asymptotic $(k^{th})$      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 $L^2(v)$      205
Parseval identity for $\mathfrak{D}_k$      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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