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Murty M.R., Esmonde J. — Problems in algebraic number theory

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Название: Problems in algebraic number theory

Авторы: Murty M.R., Esmonde J.

Аннотация:

Problem solving plays an extremely important role in strengthening mathematical research skills. The 500 problems in algebraic number theory in this work, written at varying levels of difficulty, are systemically and didactically arranged to reveal the evolution of concepts and ideas in the subject.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 2005

Количество страниц: 352

Добавлена в каталог: 22.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\mathcal{O}_K$       37
$\phi$ -function      6
$\pi(x)$       6
abc conjecture      9
Abscissa of convergence      134
Algebraic integer      27
Algebraic integer, conjugates      34
Algebraic integer, degree of      28
Algebraic integer, minimal polynomial      28
Algebraic number      27
Algebraic number field      33
Algebraic number field, degree of      33
Ambiguous ideal class      116 295
Ankeny      250
Artin character theorem      342
Artin reciprocity law      152
Artin symbol      151
Artin’s conjecture      152
Associate      13
Bateman, P.      92
Bertrand’s postulate      11 177
Brauer induction theorem      152
Brauer — Aramata theorem      155 345
Character, cubic      118
Character, cubic residue      117
Chebotarev density theorem      151
Chinese remainder theorem      60 175
Chowla      250
Class number      72
Class number formula      145
Class number, formula      137 329
Codifferent      68 242
Conjugate, complex      184
Conjugate, of an algebraic integer      34
Continued fraction, finite      108
Continued fraction, simple      108
Convergent      108
Corrales-Rodriganez, C.      173
Cubic reciprocity, law of      118 119
Cubic, character      118
Cubic, residue character      117
Cyclotomic field, discriminant      52 224
Cyclotomic field, integral basis      49 52 212 224
Cyclotomic polynomial      38 205
de la Vallee Poussin, Ch.      6
Decomposition group      151
Dedekind domain      56
Dedekind zeta function      127 146 313
Dedekind’s conjecture      345
Dedekind’s theorem      63
Different      63 68 234 242
Diophantine equations,       25 190
Diophantine equations,       74
Diophantine equations,       75 247
Diophantine equations,       8 167
Diophantine equations,       18
Diophantine equations,       8 167
Diophantine equations,       8 167
Diophantine equations,       10 174
Diophantine equations,       8 168
Diophantine equations,       17 183
Diophantine equations,       22 187
Diophantine equations,       22
Diophantine equations,       21
Diophantine equations, using Thue’s theorem      31
Dirichlet      91
Dirichlet density      149
Dirichlet, character      133
Dirichlet, class number formula      137 329
Dirichlet, hyperbola method      131
Dirichlet, L-function      133
Dirichlet, Unit Theorem      99 104
Discriminant      45
Discriminant, of a cyclotomic field      52 224
Discriminant, of a quadratic field      89 270
Discriminant, sign of      52 222
Eisenstein criterion      37 46 201
Eisenstein integers      17
Eisenstein reciprocity law      122 124
Embedding      34
Erdos, P.      9
Euclidean Domain      15 35 201
Euclidean domain, quadratic      17 18 22 25 52 181 186—189 222
Euler      6 172
Euler, $\phi$ -function      6
Fermat      8 167
Fermat, Last Theorem      8 9 167
Fermat, Last Theorem, first case      124 125
Fermat, Last Theorem, n = 3      18
Fermat, little theorem      6 161 171 174
Fermat, number      8 10 173
Fractional ideal      57
Frobenius automorphism      151
Fundamental units      99 104
Furtwangler      124
Galois extension      34
Gamma function      147
Gauss sum      84 118 136 324
Gauss’ Lemma      15 36
Germain, Sophie      11 176
Granville, A.      172
Greatest common divisor      59
Hadamard, J.      6
Hecke      132
Hecke L-function      146
Hecke, E.      146
hermite      31 79 260

Hurwitz constant      70
Hyperbola method      131
Ideal, ambiguous      116 295
Ideal, class group      72
Ideal, fractional      57
Ideal, prime      10 173
Ideal, principal      14
Index of an algebraic integer      45
Integer, algebraic      27
Integer, perfect      10
Integer, powerfull      9 171
Integer, radical of      9
Integer, squarefree      8 170
Integer, squarefull      9 171
Integral basis      43
Integral basis, construction of      51 220
Integral basis, cubic field      48
Integral basis, cyclotomic field      49 212
Integral basis, quadratic field      47
Irreducible      13
Jacobi sum      119
Jacobi symbol      95 273
Jacobi symbol, reciprocity law      96 274
Kisilevsky, H.      10 173
kronecker      100
Kronecker symbol      96 274
L-function      133
Lagrange      171
Langlands program      153
Least common multiple      60
Legendre symbol      82
Lindemann      31
Liouville’s theorem      29 34
Low, M.E.      92
Masser      9
Mersenne numbers      174
Minimal polynomial      28
Minkowski’s bound      78 256
Murty, M.R.      94
Noetherian      55
Norm map      13 67 242
Norm of an algebraic integer      41
Norm of an ideal      49
Normal closure      34
Normal extension      34
Number, algebraic      27
Number, Fermat      8 10 173
Number, Mersenne      174
Number, perfect      10
Number, transcendental      28 38 202
Oesterle      9
Perfect number      10
Polya — Vinogradov inequality      136 325
Power residue symbol      123
Powerfull      9 171
Primary algebraic integer      118 124
Prime number theorem      6
Primes in arithmetic progressions      91 134
Primitive element, theorem of      33
Primitive polynomial      16
Principal ideal      14
Principal ideal domain      14 35 201
Qadical of an integer      9
Quadratic field      88
Quadratic field, discriminant      89 270
Quadratic field, Euclidean      17 18 22 25 52 181 186—189 222
Quadratic field, integral basis      47
Quadratic field, prime decomposition      88
Quadratic field, units of      106 280 281
Quadratic field, zeta functions      130
Quadratic reciprocity, law of      87
Quadratic, nonresidue      82
Quadratic, residue      82
Ramanujan      178
Ramification      243
Ramification degree      63
Ray class group      150
Regulator      140
Relative different      68 242
Relative discriminant      68 243
Relative norm      67 241
Relative trace      67 241
Riemann hypothesis      138
Riemann zeta function      127
Roth      32
Schoof      173
Silverman      171
Split completely      151
Squarefree      8 170
Squarefull      9 171
Stickelberger’s criterion      50 214
Tensor product      52 223
thue      31 38 39 204 206
Trace map      67 242
Trace of an algebraic integer      41
Transcendental number      28 38 202
Unique factorization domain      14
Unique factorization, fractional ideals      59 229
Unique factorization, ideals in $\mathcal{O}_K$       58
Unique factorization, integers      4
UNIT      13
Vandermonde determinant      26 195 200 210
Volume of a domain      76
Volume of a lattice      105 280
Wieferich      9 124
Wilson’s Theorem      10 175 185
Zeta function, Dedekind      127 313
Zeta function, Riemann      127

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