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Dickson L.E. — History of the theory of numbers. Volume 3: quadratic and higher forms

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Название: History of the theory of numbers. Volume 3: quadratic and higher forms

Автор: Dickson L.E.

Язык:

Рубрика: История/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1992

Количество страниц: 313

Добавлена в каталог: 16.07.2005

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

Предметный указатель

"Quilibet"      54
$(a_{ij}) = matrix$       284
$(_{d}^{a} _{e}^{b} _{f}^{c})$       206
$(_{\gamma}^{\alpha} _{\delta}^{\beta})$       24 207
$E^{*}(x)$       156
$GF[p^{n}]$       293
$J(\omega)$       126
      123
$val(\omega)$       125
$\lambda$       139
$\mu (x)$       123
$\sigma (n)$ = sum divisors of n      23 227
(a, b, c)      2
(a, b, c, d)=cubic form      253
Abelian function      140—142 166 245
Aladow, J.S.      158—159
Alezais, R.      283
Algebraic numbers      2 20 29 33 38 47 70 73 86—87 90 125 159 186 192 197 200 205 258 276—278 281 see "Ternary"
Amsler, M.      53
Appell, P.      114 160
Arndt, F.      17 20 64 65 67 68 70—72 75 84 86 87 91 102 107 117 151 199 254—255
Astuti, T.      251
Asymptotic      see "Binary" "Class
Aubry, A.      47
Aubry, L.      48 79
Automorphs      see "Binary" "Quadratic "Quaternary" "Ternary"
Bachmann, P.      29 57 70 84 86 116 120 123 151 183 204 206 214—217 222 225 227 239 245 264 286 287
Bagnera, G.      221
Baker, A.L.      32
Ballantine, C.R.      301
Bauer, J.P.      232
Bauer, M.      26 44
Bazin, M.      66—68 226 232
Bell, E.T.      29 54 114 115 160 194—197 224 252
Berger, A.      111 132—133 136—137
Bernays, P.      49
Bernoulli, Jean III      5
Bernoullian numbers      55 102 124 182
Berwick, W.E.H.      257—258
Betti, E.      289
Bianchi, L.      69 199—201 204 223 232 272—273 278
Bieberbach, L.      247
Biehler, C.      114 188
Bilinear forms      129 130 240 284—288 299
Binary quadratic forms      1—205 254 see
Binary quadratic forms, $x^{2} + 27y^{2}$       55 57—59
Binary quadratic forms, $x^{2} + 2y^{2}$       3—5 7—10 15 17 19 20 23—25 29 35 37—39 42 46 47 49 51 54 56—59 134 145
Binary quadratic forms, $x^{2} + 3y^{2}$       3—5 15 17 20 23 25 29—31 35 38 42 46 47 54—59 134 162
Binary quadratic forms, $x^{2} + xy \pm y^{2}$       45 47 48 59
Binary quadratic forms, $x^{2} + y^{2}$       5 7 10 15 17 51 55—57 59 60 111 122 134—135 142—145 162 175—177 191
Binary quadratic forms, $x^{2} - 2y^{2}$       3 7 9 10 19 25 29 35 47 50 54 59 135 161 175 191
Binary quadratic forms, $x^{2} - y^{2}$       8
Binary quadratic forms, $x^{2} \pm 5y^{2}$       3 7 29 53 57 59
Binary quadratic forms, algebraic coefficients      201—202 204
Binary quadratic forms, ambiguous      13 25 28 34 48 53 64 67 77 83 85 89 90 94 120 135 145 199
Binary quadratic forms, associated      16
Binary quadratic forms, asymptotic      45 49 96 99 115 120 123 129 134 143—144 146 151 153 166 184—185 188 192 see "Median"
Binary quadratic forms, automorphs      15 23 25 41 44 93 96 124 198 201
Binary quadratic forms, character      81—88 90 199 201
Binary quadratic forms, class      14 16 26 30—33 37 40 41 49 50 53 58 63 64 69 70 73 77 79—81 83 85—90 92—197 200—205 224 246 see
Binary quadratic forms, class equations      86 148
Binary quadratic forms, class invariant, Dedekind's valence of $\omega$       125—126
Binary quadratic forms, class invariant, Kronecker's $\lambda$       139 148
Binary quadratic forms, class invariant, Kronecker's J.      126—128 130 140
Binary quadratic forms, class invariant, Weber's      86 106 148
Binary quadratic forms, complex coefficients      198—205
Binary quadratic forms, composition      60—79 82 95 122 127 155 199 204
Binary quadratic forms, compounded      61 69
Binary quadratic forms, concordant      66 69
Binary quadratic forms, conjugate      19 94
Binary quadratic forms, contains      12 13 17 25 26 46
Binary quadratic forms, continual reduction      22 49
Binary quadratic forms, correspond to ideals      70 73 87 125 159 192 197
Binary quadratic forms, decomposition      27
Binary quadratic forms, definite      17 202
Binary quadratic forms, derived      80
Binary quadratic forms, determinant      2 93 see
Binary quadratic forms, diseriminant      2 93
Binary quadratic forms, divisor      4—6 8 10 21 25 48 49 51 58 69 105 201 see "Order" "Quadratic"
Binary quadratic forms, duplication      64 67 69 82 83 85—88 199
Binary quadratic forms, equivalence      6 7 12 16 22 29 31 33 36 39 40 44 47 49 50 52 69 125—126 130—131 200—201
Binary quadratic forms, equivalence of reduced      7 9 10 14 16 24 35 40—42 53
Binary quadratic forms, equivalence, complete      37 126 129—130
Binary quadratic forms, equivalence, proper, improper      2 5 8 13 16 17 41 198
Binary quadratic forms, equivalence, relative      181
Binary quadratic forms, even, semi-even      199
Binary quadratic forms, fundamental      93
Binary quadratic forms, fundamental region      21 32 34 35 40 41 43—45 51 52 125 126 128 130—131 140—142 157 197 200
Binary quadratic forms, genera      80 82—91 94 95 104 109 155 158 199 201
Binary quadratic forms, geometrical      17 21 28 30—35 40—45 47 52 73 96—99 115 125—126 145 159 167—168 175 184—185 199—202
Binary quadratic forms, intermediate      23 32
Binary quadratic forms, invariant      35 42 46 80 see
Binary quadratic forms, invariant equation      149
Binary quadratic forms, irregular determinants      89—91
Binary quadratic forms, Kronecker form      92 138 151—153 169 179
Binary quadratic forms, linear forms of divisors      3 8—11 18 20 54
Binary quadratic forms, mean number of genera      84
Binary quadratic forms, mean number of representations      38 39 49 50 96 115 146
Binary quadratic forms, median value      83 84 95 123
Binary quadratic forms, minima      9 18 22 25 33 47 50 51 53 120 175—176 178 180 182 185—186 191—193
Binary quadratic forms, neighboring      12 15 23 24 36
Binary quadratic forms, null      39
Binary quadratic forms, number of representations      11 18 19 20 22 23 25—31 38 39 41 47 48 50 51 54 97 115 117 123 178 see
Binary quadratic forms, number of representations by a system of forms      96—97 99 115 117 123 146—147 178
Binary quadratic forms, odd      93
Binary quadratic forms, opposite      12 15 64
Binary quadratic forms, order      26 80—88 94 95 114 124 135 175
Binary quadratic forms, p-adic coefficients      202
Binary quadratic forms, parallel      78
Binary quadratic forms, period      16 23—25 31 35 37 40 42 53 64 67 85 104 188
Binary quadratic forms, polynomial coefficients      198 201
Binary quadratic forms, positive      17 73
Binary quadratic forms, primitive      80 92 138
Binary quadratic forms, principal class      64 70
Binary quadratic forms, principal, reduced      23 32 49 51 52 185—186 191 200
Binary quadratic forms, properly primitive      62 80
Binary quadratic forms, quadratic divisor      10 11 18 93 103
Binary quadratic forms, reciprocal      11
Binary quadratic forms, reduced      6 9 10 14—16 22 24 25 28 30 31 35 37 39 41 43 44 48—53 85 94 123 157 163 175 184 188 198 200—202 see "Principal"
Binary quadratic forms, reduced parallelogram      21
Binary quadratic forms, representation      2 6 11—23 25 26 28 29 31 32 34 35 38 39 41 44 49—51 54—59 66 67 81 86 99 198 201 see "Number"
Binary quadratic forms, representation belongs to root      12 14 66
Binary quadratic forms, representation by ternary      see "Ternary"
Binary quadratic forms, representation, proper, improper      2 3 5 9 77
Binary quadratic forms, representatives of classes      97 99—100 106 123—124 138 147—148 153 155 169 178 181 192
Binary quadratic forms, restricted      74 77
Binary quadratic forms, roots of      24 27 30 43 51
Binary quadratic forms, schlicht      74 77 155
Binary quadratic forms, simplest      74 82 95
Binary quadratic forms, species      198—199
Binary quadratic forms, subaltern class      126
Binary quadratic forms, symbols      93 108—109 123 127
Binary quadratic forms, tables      5 8 10 11 20 22 31 40 49 50 54 56 57 59 85 89—91 93—95 97 109 111 150 172 187—188 196
Binary quadratic forms, transformations (all) into another form      13 15—17 21 25 47—48 105 198 201
Binary quadratic forms, trinary divisor      11
Binary quadratic forms, triplication      103
Biquadratic character      17 55 57
Biquadratic reciprocity      18
Bisconcini, G.      366
Blichfeldt, H.      251
Blumenthal, O.      230
Bohler, O.      201 272
Borissow, E.      217 221
Bouniakowsky, V.      23
Bourget, H.      230 232
Brahmegupta      60
Brandt, H.      79 225—226 232
Bricard, R.      50
Brioschi, F.      290
Brix, H.      39

Bussey, W.H.      288
Byerly, W.E.      98
Cahen, E.      54 288
Cajori, F.      39
Calo, B.      287
Cantor, G.      19 29 214 221
Cauchy, A.L.      20 23 55—59 102—103 124 169 182
Cayley, A.      10 65 68 75 78 85 90 91 131 254 255
Cellerier, C.      45
Cellitti, C.      288
Cesaro, E.      38 39
Chapelon, J.      117 121—122 185—187
Charve, L.      217 218 230
Chasles, M.      131—132
Chatelain, E.      95 181
Chatelet, A.      49 287
Class number of binary quadratic forms as coefficient      124—125 134—135 143—145 160 188 190 195
Class number of binary quadratic forms as exponent of -1      103 182
Class number of binary quadratic forms by correspondence with ideals      125 159 192 197
Class number of binary quadratic forms of D in terms of h(-D)      140 153
Class number of binary quadratic forms, approximation      153 164
Class number of binary quadratic forms, arithmetical methods      134 157 184
Class number of binary quadratic forms, asymptotic mean      133—134 143 146 184—185
Class number of binary quadratic forms, asymptotic median      95 123 143—144 151
Class number of binary quadratic forms, complex coefficients      203—205
Class number of binary quadratic forms, computation formulas      157 170 188
Class number of binary quadratic forms, congruencial conditions on      94 117 151 164—165 182 see
Class number of binary quadratic forms, congruencial conditions on modulo $2^{m}$       155 171 179—180
Class number of binary quadratic forms, congruencial conditions on modulo 3      103 159
Class number of binary quadratic forms, congruencial conditions on modulo 8      164
Class number of binary quadratic forms, convention      109
Class number of binary quadratic forms, determinant negative      92—136 140—150 154—155 157—167 171—179 181—197
Class number of binary quadratic forms, determinant negative, fundamental      93 97—98 100—103 118—119 124—125 132—133 154—155 158 166—167 171—173 182
Class number of binary quadratic forms, determinant positive      94—97 99—105 107 111 115 117—120 150 185—186
Class number of binary quadratic forms, determinant positive, fundamental      100—102 107 118—119
Class number of binary quadratic forms, determinant prime      97—98 102—103 119 122 125 132—133 154 158 166—167 171—173 182
Class number of binary quadratic forms, discriminant negative      137—140 146—147 151—158 162 166—171 178—179 181 183—184
Class number of binary quadratic forms, discriminant negative, fundamental      93 137 146—147 151—158 162 169 178—179 181 183
Class number of binary quadratic forms, discriminant positive      137—140 151 153 169—170
Class number of binary quadratic forms, discriminant positive, fundamental      137 151 164
Class number of binary quadratic forms, discriminant prime      155
Class number of binary quadratic forms, discriminant, product of fundamental discriminants      169 170 179—181
Class number of binary quadratic forms, divisible by three      103 159
Class number of binary quadratic forms, even classes      127 130—132 137 142—143 150 161—162 176—177 184 189 196
Class number of binary quadratic forms, even classes, restricted by Humbert      193
Class number of binary quadratic forms, formula analogous to Gauss sums      170
Class number of binary quadratic forms, formula analogous to Lebesgue      103 118 151 155 169 171 179
Class number of binary quadratic forms, formula of Cauchy      103 124 169
Class number of binary quadratic forms, fundamental equation of Dirichlet      100 138 152—153 166 169
Class number of binary quadratic forms, fundamental formulas of Kronecker      139 148 151
Class number of binary quadratic forms, Gauss problem      95 114 see
Class number of binary quadratic forms, improperly primitive classes      99 100 103 105 107 109—110 124 126—127 135 148—150 175 181
Class number of binary quadratic forms, indefinite forms      120
Class number of binary quadratic forms, involving minima      120-121 175 186
Class number of binary quadratic forms, limit ratio of Kronecker      148 165
Class number of binary quadratic forms, linear function of divisors      186 195
Class number of binary quadratic forms, lower bound of      178
Class number of binary quadratic forms, odd classes      111—116 121—125 130 133—136 143—144 147 160—162 175—177 185—197 see
Class number of binary quadratic forms, odd classes, Humbert's restricted      192—193
Class number of binary quadratic forms, odd classes, Joubert's restricted      111
Class number of binary quadratic forms, parity      94 107 117 151 155 164—165 179 see
Class number of binary quadratic forms, primitive      138—140 146—147 152—159 163—164 168—171 178—181 183—184
Class number of binary quadratic forms, product of class numbers      171
Class number of binary quadratic forms, properly primitive      97—104 107 111 115 117—120 122—127 132—133 135 148 150 154—155 159—160 163—168 172—174 178—179 181—182
Class number of binary quadratic forms, ratio of class numbers for different orders      109 114 124 135 148 175 203—205 see
Class number of binary quadratic forms, recurrence formula      191 195 see
Class number of binary quadratic forms, relations      92 105—106 108—117 121—122 124—125 128—138 140—145 149—150 160—162 174—177 185—191 195—197 see
Class number of binary quadratic forms, relations involving indefinite form      135 162 175 191
Class number of binary quadratic forms, relations involving minima      176—178 180 186 193
Class number of binary quadratic forms, relations of grade eight      128 140
Class number of binary quadratic forms, relations of grade eleven      132 137—138
Class number of binary quadratic forms, relations of grade five      127 132 150 186—187
Class number of binary quadratic forms, relations of grade four      128
Class number of binary quadratic forms, relations of grade one      126 130 140 149
Class number of binary quadratic forms, relations of grade q a prime      140—142 150
Class number of binary quadratic forms, relations of grade seven      128 132 141—142
Class number of binary quadratic forms, relations of grade sixteen      128
Class number of binary quadratic forms, relations of grade thirteen      132
Class number of binary quadratic forms, relations of grade three      132 150 177 191
Class number of binary quadratic forms, relations of grade two      106 128 161 191
Class number of binary quadratic forms, relations, arithmetical deduction      114—117 174 183 185 190 197
Class number of binary quadratic forms, relations, Kronecker — Hurwits type of      124—125 145 162 175
Class number of binary quadratic forms, relations, Liouville's first type of      121 161 175
Class number of binary quadratic forms, relations, Liouville's second type of      121 161 175
Class number of binary quadratic forms, relations, reversion of      195—196
Class number of binary quadratic forms, same formula for $Cl(D_{0})$ and $Cl(-D_{0})$       139 152
Class number of binary quadratic forms, similar formulas for h(D) and h(-D)      119
Class number of binary quadratic forms, square of class number      171 173
Class number of binary quadratic forms, sum of      133 136 143—144 147 158 168—170 184
Class number of binary quadratic forms, unity      163—164 183—184 186
Class number of binary quadratic forms, upper bound of      172—174
Classes of forms modulo p      294—295
Clausen, C.      145
Clausen, T.      55
Cogredient      130 285—286 297 301
Combinants      295
Conics modulo p      297 299
Continued fractions      10 15 16 18 19 21 24—26 28 30 32 33 35 37 41 44 48 49 51 53 54 200—201 219
Cotty, G.      202 230 232
Covariant      33 293—301
Cresse, G.H.      185 197
Crystallography      224
Cubic curves modulo p      297
Cubic forms      253—268
Cubic forms and algebraic numbers      258
Cubic forms modulo p      299—301
Cubic forms tables      255 258
Cubic residue      58 159 292
Cubic residue, surfaces modulo p      299
Cunningham, A.      10 46 53 54 59
Cyclotomy      55—58 98 102 117—118 151 166 170—173 179
De Helguero, F.      48
De Jouquieres, E.      32 46
de la Vallee Poussin, Ch.      44 87 188
de Polignac, A.      290
De Seguier, J.A.      86 95 139 140 151—153 158 299
Decomposable forms      235—236 259 261 263—266
Dedekind, R.      2 32 35 39 41 44 60 69 70 73 75 76 78 79 83 86 87 92 95—97 119 122 125—126 149 150 159 165 172 179 197 204 264
Delaunay, B.      258
Determinant      68 78 155 236 268 290—291 294 296 see "Forms" "Ternary"
Dickson, L.E.      47 95 183—184 214 247—248 251 268 283 287—292 293-301
Diophantus      60
Dirichlet series      97 128—129 138—140 147—148 157 165 188 192
Dirichlet, G.L.      1 13 16—21 24—29 31 35 36 38 40 41 44 51 60 66 68 77 81 83—87 92 95 97—105 107 109 111 115 117—119 122 124 129 136—140 146—148 150—151 153—154 156—159 162 164—167 169—170 172—175 178—179 181—182 188 192 195 198—200 203—206 210 212 222 224 229 242 250 265 273 275
Divisors, functions of      23 29 108—109 115 122 128 130—131 136 142 176—177 180—181 186 189 193 196
d|m      168
E(D)=fundamental unit      138
Eisenstein, G.      34 57 59 80 88 103 204 206 210 211 213—217 222—223 225 228 234 236 238 241 253—254 258 259 261—263 284
Elementary chord      42
Elementary divisor      285
Elementary triangle      42 167
Elliptic function      20 105 106 108—109 113 121 134 136 162 185—186 204
Elliptic function, complex multiplication of      105 120 151
Elliptic modular function      32 36 125—128 130—131 140—141 148 150 197
Elliptic modulus      94 105—111 120 126
Epstein, P.      53
Equivalent numbers      32 44 53
Equivalent numbers, relatively      128 140—141
Erler, H.W.      64 103—104
Euler's constant      45 84 146 164 184
Euler, L.      1 3—5 7 9 15 22 60 146 164 184 206 225 226
Factoring      8
Farey series      42 43 53
Fatou, P.      273 274 276
Felstein, M.M.      301
Fermat      1—3 8 15 206
Fields, J.C.      39
Fontene, G.      48
Form problem      296
Forms never $\equiv 0 (mod \ p)$       292

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