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Hans Rademacher — Lectures on elementary number theory

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Название: Lectures on elementary number theory

Автор: Hans Rademacher

Аннотация:

Using a background of analysis and algebra, the reader is led to the fundamental theorems of number theory; the uniqueness of prime number factorization and the reciprocity law of quadratic residues. Cyclotomy is treated in some detail because of its own significance and as a framework for the elegant theorems on Gaussian sums. Asymptotic laws are discussed as a foretaste of analytic number theory; also, Dirichlet's theorem about primes in an arithmetic progression and V. Brun's theorem on twin primes.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1964

Количество страниц: 152

Добавлена в каталог: 19.11.2012

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Предметный указатель

0(x) order of magnitude      98
Abel      59 117
Abelian groups      18
Approximation      39
Asymptotic to      112
Binomial coefficient      85
Brun, Viggo      137
Buniakovski      111
Cardano      59
CHARACTER      72 80 89 123
Character, principal      123
chebyshev      112 116 118
Chinese remainder theorem      22
Coefficient, binomial      85
Coefficient, Fourier      77 78
Common fractions      6 7
Congruence      17 21
Coprime      2
Cyclotomic equation      52 59 62 67
Cyclotomic polynomial      61
De La Vallee Poussin      112
Diophantine equation      12
Dirichlet      2 31 121
Dirichlet series      129
Divisors, number of      100
Elementary symmetric function      141
Equivalence relation      6 17
Erdoes      61 112
Euclid      1 5
Euclid's lemma      11 15
Euler      21 30 58 109 120 121
Euler function      18 20 105
Euler product      107
Euler — Mascheroni constant      99
Euler'a criterion      72
Farey sequence      8 32 42
Fermat      3 21 30 58 68 73
Ferrari      59
Ford circles      41
Fourier coefficient      77 78
Fourier series, finite      76
Fractions, common      6 7
Fractions, partial      19
Function, elementary symmetric      141
Function, Euler      18 20 105
Function, Moebius      103 108
Function, zeta      107
Gauss      3 53 58 112
Gaussian polynomials      83 84 85
Gaussian sum      42 54 70 75 80 83 86 91
Gaussian sumá sign of      93
Goldbach's problem      144
Greatest common divisor      15
Group character      123 125
Group, abelian      122
hadamard      112
Hardy      100 144
Heptadecagon      52
Higher congruences      21

Hurwitz      40 47
INDEX      65
Irrational number      15 31 39
Jacobi symbol      88 90 95 109
Lagrange resolvent      63 68
Landau      100
Lattice points      97
Lattice points in a circle      99
Least common multiple      15
legendre      113
Legendre symbol      71 82
Length of decimal period      27 52
Littlewood      144
Mediant      10
Moebius function      103 108
Monic polynomial      61
Nielandt      100
Partial fractions      19
Partial summation      117 118
Period (Gauss)      53 64
Periodic decimals      24 26
Pigeon-hole principle      31
Polynomial, cyclotomic      52 59 62 67
Polynomial, Gaussian      83 84 85
Polynomial, monic      61
Prime factorization      5
Prime factorization, uniqueness      13 14
Prime number theorem      112
Primes in arithmetic progression      2 34 36 135
Primitive congruence root      49
Quadratic forms      38
Quadratic reciprocity theorem      73 79
Quadratic residues      70
Reciprocity      73 79 93 109
Reflexivity      6 17
Riemann      107
Root of unity      60
Schnirelmann      144
Selberg      112 144
Sierpinski      100
Sieve of Eratosthenes      137
Subgroup      29
Symbol, Jacobi      88 90 95 109
Symbol, Legendre      71 82
Symmetry      6 17
Theorem, Chinese remainder      22
Theorem, prime number      112
Theorem, quadratic reciprocity      73 79
Theorem, Wilson's      2 22
Transcendental      83 92
Transitivity      6 17
Twin primes      4 137 143
Uniqueness of prime factorization      13
van der Corput      100
Vinogradov      144
voronoi      102
Waring      2
Wilson's theorem      2 22
Zeta-function      107

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