Swinnerton-Dyer H.P.F. — A brief guide to algebraic number theory :: Электронная библиотека попечительского совета мехмата МГУ

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Swinnerton-Dyer H.P.F. — A brief guide to algebraic number theory

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Название: A brief guide to algebraic number theory

Автор: Swinnerton-Dyer H.P.F.

Аннотация:

A text primarily for beginning graduate students that is largely an account of mainstream theory but also contains some illustrative applications. Algebraic number theory, originally developed to attack Fermat's Last Theorem, has become an important tool over a wide range of pure mathematics, and many of the ideas involved generalize to branches such as algebraic geometry. The text covers the two basic methods of approaching algebraic number theory: using ideals and valuations. The author is a Cambridge (UK) mathematician.

Язык:

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 146

Добавлена в каталог: 12.06.2005

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Предметный указатель

$d_{k}$       4
$J_{k}$       15 50
$k_{\mathfrak{p}}$       34
$r_{1}$ , $r_{2}$       3
$V_{k}$       49
$\Delta^{2}$       4
$\mathcal{C}_{k}$       15
$\mathcal{S}_{k}$       16
$\mathfrak{o}$ , $\mathfrak{O}$       1
$\omega$       53
Absolute norm      13
Absolute value      31
Adele      48
Adele, principal      49
Algebraic number field      vii
Approximation, strong      40
Approximation, weak      39
Archimedean      32
Artin element, symbol      29
Artin map      100
Artin map, local      108
Artin reciprocity law      100
Ascending chain condition      6
Cebotarev density theorem      96
CHARACTER      125
Character, congruence      79
Character, Hecke Groessencharakter      82 90 104
Character, Tate      84
Characteristic polynomial      121
Chinese remainder theorem      12
Circle group      125
Class field      99
Class field theory      viii
Class number      15
Conductor      43 68 99 100
Congruence divisor class group      99
Conorm      23
Cyclotomic      65
Dedekind domain      9
density      94
Density, Dirichlet      94
Diagonal map      49 51
Different      43 44
Different, local      44
Discriminant, absolute      4
Discriminant, relative      26
Exercise      17 19 40 43 62 69 76 111
Fermat's last theorem      vii 73
First degree primes      94
Frobenius element      29 134
Gauss sum      69
H      15
Haar measure, integral      123
Hasse norm theorem      102

Height      16
Hensel's lemma      35
Hilbert basis theorem      8
Hilbert symbol      107 108
Hilbert's theorem      90 4
Ideal class group      15
Ideal, fractional      10
Ideal, integral      10
Idele      48 50
Idele class group      105
Idele, principal      51
Inertia group, field      28
Integer, algebraic      1146
Integral at p      14
Integral closure      3
Kronecker — Weber Theorem      viii 112
L-series, Dirichlet      79
Lattice      120
Local field      35
Minimal base      118
Noetherian      6
Norm      121
Order      3
Pigeonhole Principle      16 120
Place      31
Place, finite      34
Place, infinite      33
Pontryagin duality      125
Power residue symbol      106
Product formula      35 50
Quadratic reciprocity law      61
Quasi-character      128
R      23
Ramification      41
Ramification group      28
Ramification, tame      41
Ramification, wild      41
Ramified primes      15
Reduced form      57
Regulator      23
Riemann hypothesis      79
Splitting group, field      27
Stickelberger      5
t      125
Trace      121
Transform, Fourier      128
Transform, Mellin      130
Ultrametric      34
UNIT      15
Unit, cyclotomic      71
Unit, fundamental      58
Valuation, additive      35
Valuation, multiplicative      31
Zeta function, Riemann      79
Zeta function, Tate      84

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