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Stewart I., Tall D. — Algebraic Number Theory and Fermat's Last Theorem
Stewart I., Tall D. — Algebraic Number Theory and Fermat's Last Theorem



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Название: Algebraic Number Theory and Fermat's Last Theorem

Авторы: Stewart I., Tall D.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Edition

Год издания: 2001

Количество страниц: 336

Добавлена в каталог: 04.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal{L}$-periodic      245
(a, b, c) Conjecture      267
a-powered number      265
ABC-Conjecture      267
Abel, Niels Henrik      243 263
Addition theorem      243
Affine plane      216
Al-Khowarizmi, Mohammed      1
Algebra      1
algebraic      4 21 36
Algebraic integer      4 9 35 42 43 73
Algebraic number      35 43
Algebraic number held      35
Algebraically closed      13
Algorithm, division      14
Algorithm, Euclidean      15
Analytic class-number formula      197
Ascending chain condition      80
Associate      76
Automorphic function      205
Babylonian      1
Basic exponent      266
Basis      27 45
Beal Conjecture      267
Beal, Andrew      267
Bernoulli number      197 198
Beukers, Frits      264
Bezout’s Theorem      227
Bilinear map      251
Birkhoff, George      203
Bounded      129
Breuil, Christophe      263
Carcavi, Pierre de      143
Cardano, Girolamo      2
Catalan conjecture      264
Catalan problem      263
Cauchy, Augustin-Louis      243 274
Centrally symmetric      139
Characteristic      13
Class number problem      179
Class-group      151 152 157
Class-number      151 152 157 176 177 197
Coates, John      208 209
Complex line      213
Complex projective line      218
Complex projective plane      218
Complex projective point      218
Conductor      260
conformal      251 255
conic      214 215
Conic section      214
conjugate      38
Conrad, Brian      263
Constant      14
Convex      139
Coprime      15 89
Cubic      14
Cusp      223 256
Cusp form      259 262
Cyclotomic field      122
Cyclotomic number field      256
Darmon, Henri      264
Dedekind ring      106
Dedekind zeta-function      197
Dedekind, Richard      5 101 102 105 201
Degree      14 20
Diamond, Frederick      263
Dickson, Leonard Eugene      93 201
DIMENSION      129
Diophantine equation      xi 1 96 222 230 243 263 266
Diophantus      2 235
Diophantus of Alexandria      xi 1
Dirichlet L-series      197
Dirichlet, Peter Lejeune      185 293
Dirichlet’s units theorem      293 296 300
Discrete      130
Discriminant      38 40 46 48 63 68 115 155 207 248 260
Distance      149
Divide      13
Domain      10 12 79
Domain, Euclidean      90 91
Domain, noetherian      80
Domain, principal ideal      90
Domain, unique factorization      89—91
Doubly periodic      244 246 247
Eigenform      259
Eisenstein series      247
Eisenstein, F.G.      75 87 274
Eisenstein’s Criterion      18 64
Elkies, Noam      231
Elliptic curve      205 213 222 224 248 250 258 259
Elliptic curve, group structure on an      226
Elliptic function      235 243
Elliptic integral      243 244
Elliptic modular function      235 254 256
Equivalent      152
Euclidean function      90 91
Euler function      276
Euler, Leonhard      3 73 75 143 144 184 257 273 276
Euler’s conjecture      230
Euler’s criterion      284
EXPONENT      277
Extension, finite      21
Factor      13
Factor, proper      13
Factorization      10 13 18 35 73 80—82 121 169
Faltings, Gerd      209—211
Fermat equation      186 193 262
Fermat — Catalan Conjecture      264 268
Fermat, Pierre de      2 6 75 94 143 144 183 186 257
Fermat’s Last Theorem      xii 2 3 5 6 9 75 151 183 196 201 205 208 250 256 257 262 263 267 274
Fermat’s Last Theorem, n=4      186
Fermat’s Last Theorem, sketch proof of      261
Field      10 12
Field extension      20
Field of fractions      12
Field polynomial      39 40
Field, cyclotomic      64
Field, Gaussian      63
Field, quadratic      61 91 169
Finitely generated      12
Finitely generated R-module      25
Flach, Mattheus      209 211
Fleck, Albert      202
Formal derivative      16
Four-squares theorem      143
Fractional ideal      101
Frey curve      207 208 260
Frey elliptic curve      235 256 257 262
Frey, Gerhard      207 257
Frye, Roger      232
Function, doubly periodic      242
Function, meromorphic      244
Fundamental domain      131 132 154 253
Galois, Evariste      263
Gauss, Carl Friedrich      3 4 75 86 179 243 273 284 286 288
Gaussian integer      4 63 75
Gauss’s criterion      285
Generate      11 25 129
Genus      204 262
Geometric representation      148
Germain, Sophie      184 201
Godfield, Dorian      179
Granville, Andrew      264
Greatest common divisor      114
Gross, Benedict      179
Group, abelian      275
Group, additive      26
Group, circle      132
Group, finitely generated abelian      27 32
Group, free abelian      26 28 129
Group, of units      77 295 300
Group, symmetric      22
Hecke operators      259
Hellegouarch, Yves      257
Highest common factor      15
Hilbert, David      5 161
Homogeneous coordinates      218 219
Hornomorphism      11
Ideal      11 102 103 201
Ideal number      5 101 102 151 201
Ideal, fractional      107 110 151
Ideal, maximal      105
Ideal, prime      105 107 110
Ideal, principal      158
Image      11
INTEGER      45 62
Integral basis      46 63
Integral domain      10
Invariant      251
Irreducible      14 17 74 80 82 87
Isomorphism      11
J-invariant      260 261
Jacobi, Carl Gustav Jacob      243 274
Jensen, Johann Ludwig Wilhelm Waldemar      185
Katz, Nick      210
Kernel      11
Kronecker, Leopold      274
Kummer, Ernst      3 5 75 101—103 123 151 162 183 185 196 201 203 274
Kummer’s Lemma      189 191
Kummer’s Theorem      193
Lagrange, Joseph-Louis      144 184
Lame, Gabriel      5 75 185
Langlands, Robert      211
Lattice      129 130 140 153 245 246 251 252 296 298
Least common multiple      114
Legendre normal form      249
Legendre symbol      281 289
Legendre, Adrien-Marie      3 185 201 243 244 249 273 283
Length      149
Level      256 262
Level Reduction Conjecture      262
Lexicographic order      24
Lindeinann, Ferdinand      202
Line at infinity      216
Linear      14
Linearly independent      27
Liouville, Joseph      5 185 250 274
Local coordinate map      255
Logarithmic representation      295
Logarithmic space      294 295
Lowest common multiple      89
Maximal condition      80
Mazur, Barry      230
Meromorphic      246
Mersenne, Marin      143
Minimal discriminant      260
Minimum polynomial      21 40 64
Minkowski, Hermann      139 142
Minkowski’s constants      172 175
Minkowski’s theorem      140 142 145 151 153 154 173 175 293 295
Mirimanoff, Dimitri      186 201
Miyaoka, Yoichi      209
Mobius map      251
Mobius transformation      205
Modular      258 259 262
Modular curve      256
Modular domain      253
Modular form      262
Modular function      205 250 261
Modular group      252
Monic      21
Monomorphism      11 38
Mordell conjecture      204 205
Mordell, Louis      204
Mordell’s theorem      229
Multi-valued      254
Multiplicity      16
Nagell, Trygve      96
Newton, Isaac      222
Noether, Emmy      80
Non-singular      223
Norm      49 82 115 146
Norm-Euclidean      93
Normal form      214 215
Number field      36
Overlap map      255
Parallel line      217
Parametrization      238 243 248
Parametrize      259
Patch      255
Period parallelogram      245
Poincare, Henri      204 205
Point at infinity      216
Pole      242
Polynomial      14
Polynomial, elementary symmetric      23
Polynomial, symmetric      22
Prime      3 74 75 87 142 169
Prime factorization      110
Prime number      73
Prime subfield      13
Prime, regular      193
Primitive root      276
Principal fractional ideal      152
Principal ideal      12 103 116
Projection      216
Projective line      215
Projective point      215
Projective special linear group      252
Projective transformation      216
Projectively equivalent      216
Pythagoras      xi 1 129
Pythagorean      1
Pythagorean equation      236 238 239 241 243
Pythagorean triad      1 2
Pythagorean triple      222 266
Quadratic      14
Quadratic reciprocity      204
Quadratic reciprocity law      273 286
Quadratic residues      273 283
Quartic      14
Quintic      14
Quotient module      25
Quotient ring      11
R-action      25
R-module      25
R-submodule      25
Radical      265
Ramanujan — Nagell Theorem      96
Ramanujan, Srinivasa      96
Rank      28
Rational conic      220
Rational elliptic curve      225
Rational integer      45
Rational line      220
Rational point      220
Real elliptic curve      225
Real projective plane      215
Reciprocity      3
Reducible      13
Reduction      19 258
Regular      193 198 223
Regular prime      5 185
Regulator      197
Residue      242
Residue, biquadratic      4
Residue, cubic      54
Residue, quadratic      3
Ribet, Kenneth      257 262
1 2
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