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Borevich Z.I., Shafarevich I.R. — Number Theory
Borevich Z.I., Shafarevich I.R. — Number Theory



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Название: Number Theory

Авторы: Borevich Z.I., Shafarevich I.R.

Аннотация:

This is a english translation of first edition "Боревич З.И., Шафаревич И.Р. Теория чисел". from translator's preface:
This book was written as a text for the learning of number theory, not as
a reference work, and we have attempted to preserve the informal, slow-placed style of the original. The emphasis of the book is on number theory as a living branch of modern mathematics, rather than as a collection of miscellaneous results.


Язык: en

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 439

Добавлена в каталог: 20.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute index of ramification of divisor      217
Absolute norm of divisor      216
Absolute norm of divisor, degree of inertia      217
Absolutely irreducible polynomial      10
Algebraic element, extension      396
Algebraic element, number      78
Algebraic integer      92
Algebraic number field      78
Analytic curve      305
Analytic curve, function      284
Associate numbers of module      89
Basis of field extension      397
Basis of lattice      99
Basis of module      83
Bernoulli number      382
Binary quadratic form      395
Bounded p-adic sequence      28
Bounded set of points      100
Centrally symmetric set      110
Character of Abelian group      415
Character of quadratic field      238
Characteristic polynomial      399
Class of divisors      220
Coefficient ring      87
Complete field under valuation      255
Complete metric field      35
Completion of field, under metric      35
Completion of field, under valuation      253
Congruence of elements of ring modulo a divisor      207
Congruence of polynomials      3
Conjugate fields      404
Conjugate fields, elements      404
Convex set      110
Cyclotomic field      325
Cyclotomic polynomial      325
Decomposable form      78
Dedekind ring      207
Degree of field extension      396 397
Degree of inertia, of extension of field with valuation      259
Degree of inertia, of prime divisor      199
Determinant of quadratic form      390
Diagonal quadratic form      392
Direct sum of quadratic forms      392
Dirichlet series      330
Discrete set of points      99 100
Discriminant of algebraic number field      92
Discriminant of basis      403
Discriminant of binary quadratic form      139
Discriminant of full module      92
Division with remainder      166
Divisor      170 212
Dual basis      403
Equivalence of divisors      220 221
Equivalence of integral polynomials modulo a prime      3
Equivalence of quadratic forms      391
Euclidean ring      166
Even numerical character      335
Extension field      396 397
Extension of valuation      185
Finite extension of field      397
Finite prime divisor      280
Fractional divisor      212
Full decomposable form      83
Full lattice      99
Full module      83
Fundamental basis of finite extension of field with valuation      260
Fundamental basis of integral closure      200
Fundamental domain      312
Fundamental modulus of numerical character      420
Fundamental parallelepiped      101
Fundamental sequence      34
Fundamental units of algebraic number field      114
Gaussian sum      14 333
Genus of divisor      245
Genus of form      241
Hilbert symbol      55
Ideal of field relative to Dedekind ring      214
Index of finite extension of field with valuation      259
Index of ramification of prime divisor      196
Index of valuation      186
Inertia field of finite extension      263
Infinite prime divisor      280
Integral closure      413
Integral divisor      212 213
Integral element of field with valuation      255
Integral element over ring      412
Integral element over valuation      181
Integral equivalence of forms      77
Integrally closed      413
Invariants of finite Abelian group      415
Irregular prime number      224
Lattice      99
Local analytic manifold      302
Local method      251
Logarithmic representation of algebraic numbers      104
Metric      33
Metric field      32
Minimum polynomial      397
Modular equivalence      149
Module in algebraic field      81
Norm of divisor      198
Norm of element      400
Norm of module      124
Norm of point      98
Normed Gaussian metric      281
Normed Gaussian sum      349
Numerical character      418
Odd numerical character      335
Order in algebraic number field      88
p-Adic completion      253
p-Adic field      25 35 280 281
p-Adic field, field of formal power series      40 263
p-Adic integer      20
p-Adic metric      27 277
p-adic valuation      23 178
p-Integral rational number      22
Prime divisor      170 171
Prime element of ring      165
Primitive character      419
Primitive element of algebraic number field      79
Primitive element of finite extension      398
Primitive form      140
Primitive polynomial      275
Principal divisor      170 171
Proper equivalence of binary quadratic forms      140
Quadratic field      130
Quadratic numerical character      17 237 349
Reduced number of imaginary quadratic field      148
Reduced number of real quadratic field      153
Reduced number, basis of planar lattice      145
Reduced number, module of imaginary quadratic field      148
Reduced number, module of real quadratic field      153
Regular prime number      224
Regulator of algebraic number field      115
Regulator of order      115
Representation of number by quadratic form      391
Representation of zero by quadratic form      391
Residue class field of field with valuation      255
Residue class field of valuation      181
Ring of residue classes modulo a divisor      208
Ring of valuation      187
Separable extension      402
Similar modules      82
Simple finite extension      185 186
Strict equivalence of divisors of quadratic field      239
Strictly similar modules in quadratic field      140
Suitable numbers of Euler      427
Topological isomorphism      35
Totally ramified extension of field with valuation      262
Trace of element      400
Transcendental element      397
Unique factorization      166
Unit of algebraic number field      93
Unit of order      93
Unit, p-adic      21
Unramified extension of field with valuation      262
Valuation      175
Zeta-function of Dedekind      309
Zeta-function of Riemann      320
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