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

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

јвтор: Dickson L.E.

язык: en

–убрика: »стори€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1992

 оличество страниц: 313

ƒобавлена в каталог: 16.07.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный 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
$Of(x)$      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      140Ч142 166 245
Aladow, J.S.      158Ч159
Alezais, R.      283
Algebraic numbers      2 20 29 33 38 47 70 73 86Ч87 90 125 159 186 192 197 200 205 258 276Ч278 281 see "Ternary"
Amsler, M.      53
Appell, P.      114 160
Arndt, F.      17 20 64 65 67 68 70Ч72 75 84 86 87 91 102 107 117 151 199 254Ч255
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 214Ч217 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.      66Ч68 226 232
Bell, E.T.      29 54 114 115 160 194Ч197 224 252
Berger, A.      111 132Ч133 136Ч137
Bernays, P.      49
Bernoulli, Jean III      5
Bernoullian numbers      55 102 124 182
Berwick, W.E.H.      257Ч258
Betti, E.      289
Bianchi, L.      69 199Ч201 204 223 232 272Ч273 278
Bieberbach, L.      247
Biehler, C.      114 188
Bilinear forms      129 130 240 284Ч288 299
Binary quadratic forms      1Ч205 254 see
Binary quadratic forms, $x^{2} + 27y^{2}$      55 57Ч59
Binary quadratic forms, $x^{2} + 2y^{2}$      3Ч5 7Ч10 15 17 19 20 23Ч25 29 35 37Ч39 42 46 47 49 51 54 56Ч59 134 145
Binary quadratic forms, $x^{2} + 3y^{2}$      3Ч5 15 17 20 23 25 29Ч31 35 38 42 46 47 54Ч59 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 55Ч57 59 60 111 122 134Ч135 142Ч145 162 175Ч177 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      201Ч202 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 143Ч144 146 151 153 166 184Ч185 188 192 see "Median"
Binary quadratic forms, automorphs      15 23 25 41 44 93 96 124 198 201
Binary quadratic forms, character      81Ч88 90 199 201
Binary quadratic forms, class      14 16 26 30Ч33 37 40 41 49 50 53 58 63 64 69 70 73 77 79Ч81 83 85Ч90 92Ч197 200Ч205 224 246 see
Binary quadratic forms, class equations      86 148
Binary quadratic forms, class invariant, Dedekind's valence of $\omega$      125Ч126
Binary quadratic forms, class invariant, Kronecker's $\lambda$      139 148
Binary quadratic forms, class invariant, Kronecker's J.      126Ч128 130 140
Binary quadratic forms, class invariant, Weber's      86 106 148
Binary quadratic forms, complex coefficients      198Ч205
Binary quadratic forms, composition      60Ч79 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      4Ч6 8 10 21 25 48 49 51 58 69 105 201 see "Order" "Quadratic"
Binary quadratic forms, duplication      64 67 69 82 83 85Ч88 199
Binary quadratic forms, equivalence      6 7 12 16 22 29 31 33 36 39 40 44 47 49 50 52 69 125Ч126 130Ч131 200Ч201
Binary quadratic forms, equivalence of reduced      7 9 10 14 16 24 35 40Ч42 53
Binary quadratic forms, equivalence, complete      37 126 129Ч130
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 43Ч45 51 52 125 126 128 130Ч131 140Ч142 157 197 200
Binary quadratic forms, genera      80 82Ч91 94 95 104 109 155 158 199 201
Binary quadratic forms, geometrical      17 21 28 30Ч35 40Ч45 47 52 73 96Ч99 115 125Ч126 145 159 167Ч168 175 184Ч185 199Ч202
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      89Ч91
Binary quadratic forms, Kronecker form      92 138 151Ч153 169 179
Binary quadratic forms, linear forms of divisors      3 8Ч11 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 175Ч176 178 180 182 185Ч186 191Ч193
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 25Ч31 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      96Ч97 99 115 117 123 146Ч147 178
Binary quadratic forms, odd      93
Binary quadratic forms, opposite      12 15 64
Binary quadratic forms, order      26 80Ч88 94 95 114 124 135 175
Binary quadratic forms, p-adic coefficients      202
Binary quadratic forms, parallel      78
Binary quadratic forms, period      16 23Ч25 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 185Ч186 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 14Ч16 22 24 25 28 30 31 35 37 39 41 43 44 48Ч53 85 94 123 157 163 175 184 188 198 200Ч202 see "Principal"
Binary quadratic forms, reduced parallelogram      21
Binary quadratic forms, representation      2 6 11Ч23 25 26 28 29 31 32 34 35 38 39 41 44 49Ч51 54Ч59 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 99Ч100 106 123Ч124 138 147Ч148 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      198Ч199
Binary quadratic forms, subaltern class      126
Binary quadratic forms, symbols      93 108Ч109 123 127
Binary quadratic forms, tables      5 8 10 11 20 22 31 40 49 50 54 56 57 59 85 89Ч91 93Ч95 97 109 111 150 172 187Ч188 196
Binary quadratic forms, transformations (all) into another form      13 15Ч17 21 25 47Ч48 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 225Ч226 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 55Ч59 102Ч103 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 121Ч122 185Ч187
Charve, L.      217 218 230
Chasles, M.      131Ч132
Chatelain, E.      95 181
Chatelet, A.      49 287
Class number of binary quadratic forms as coefficient      124Ч125 134Ч135 143Ч145 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      133Ч134 143 146 184Ч185
Class number of binary quadratic forms, asymptotic median      95 123 143Ч144 151
Class number of binary quadratic forms, complex coefficients      203Ч205
Class number of binary quadratic forms, computation formulas      157 170 188
Class number of binary quadratic forms, congruencial conditions on      94 117 151 164Ч165 182 see
Class number of binary quadratic forms, congruencial conditions on modulo $2^{m}$      155 171 179Ч180
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      92Ч136 140Ч150 154Ч155 157Ч167 171Ч179 181Ч197
Class number of binary quadratic forms, determinant negative, fundamental      93 97Ч98 100Ч103 118Ч119 124Ч125 132Ч133 154Ч155 158 166Ч167 171Ч173 182
Class number of binary quadratic forms, determinant positive      94Ч97 99Ч105 107 111 115 117Ч120 150 185Ч186
Class number of binary quadratic forms, determinant positive, fundamental      100Ч102 107 118Ч119
Class number of binary quadratic forms, determinant prime      97Ч98 102Ч103 119 122 125 132Ч133 154 158 166Ч167 171Ч173 182
Class number of binary quadratic forms, discriminant negative      137Ч140 146Ч147 151Ч158 162 166Ч171 178Ч179 181 183Ч184
Class number of binary quadratic forms, discriminant negative, fundamental      93 137 146Ч147 151Ч158 162 169 178Ч179 181 183
Class number of binary quadratic forms, discriminant positive      137Ч140 151 153 169Ч170
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 179Ч181
Class number of binary quadratic forms, divisible by three      103 159
Class number of binary quadratic forms, even classes      127 130Ч132 137 142Ч143 150 161Ч162 176Ч177 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 152Ч153 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 109Ч110 124 126Ч127 135 148Ч150 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      111Ч116 121Ч125 130 133Ч136 143Ч144 147 160Ч162 175Ч177 185Ч197 see
Class number of binary quadratic forms, odd classes, Humbert's restricted      192Ч193
Class number of binary quadratic forms, odd classes, Joubert's restricted      111
Class number of binary quadratic forms, parity      94 107 117 151 155 164Ч165 179 see
Class number of binary quadratic forms, primitive      138Ч140 146Ч147 152Ч159 163Ч164 168Ч171 178Ч181 183Ч184
Class number of binary quadratic forms, product of class numbers      171
Class number of binary quadratic forms, properly primitive      97Ч104 107 111 115 117Ч120 122Ч127 132Ч133 135 148 150 154Ч155 159Ч160 163Ч168 172Ч174 178Ч179 181Ч182
Class number of binary quadratic forms, ratio of class numbers for different orders      109 114 124 135 148 175 203Ч205 see
Class number of binary quadratic forms, recurrence formula      191 195 see
Class number of binary quadratic forms, relations      92 105Ч106 108Ч117 121Ч122 124Ч125 128Ч138 140Ч145 149Ч150 160Ч162 174Ч177 185Ч191 195Ч197 see
Class number of binary quadratic forms, relations involving indefinite form      135 162 175 191
Class number of binary quadratic forms, relations involving minima      176Ч178 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 137Ч138
Class number of binary quadratic forms, relations of grade five      127 132 150 186Ч187
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      140Ч142 150
Class number of binary quadratic forms, relations of grade seven      128 132 141Ч142
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      114Ч117 174 183 185 190 197
Class number of binary quadratic forms, relations, Kronecker Ч Hurwits type of      124Ч125 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      195Ч196
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 143Ч144 147 158 168Ч170 184
Class number of binary quadratic forms, unity      163Ч164 183Ч184 186
Class number of binary quadratic forms, upper bound of      172Ч174
Classes of forms modulo p      294Ч295
Clausen, C.      145
Clausen, T.      55
Cogredient      130 285Ч286 297 301
Combinants      295
Conics modulo p      297 299
Continued fractions      10 15 16 18 19 21 24Ч26 28 30 32 33 35 37 41 44 48 49 51 53 54 200Ч201 219
Cotty, G.      202 230 232
Covariant      33 293Ч301
Cresse, G.H.      185 197
Crystallography      224
Cubic curves modulo p      297
Cubic forms      253Ч268
Cubic forms and algebraic numbers      258
Cubic forms modulo p      299Ч301
Cubic forms tables      255 258
Cubic residue      58 159 292
Cubic residue, surfaces modulo p      299
Cunningham, A.      10 46 53 54 59
Cyclotomy      55Ч58 98 102 117Ч118 151 166 170Ч173 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 151Ч153 158 299
Decomposable forms      235Ч236 259 261 263Ч266
Dedekind, R.      2 32 35 39 41 44 60 69 70 73 75 76 78 79 83 86 87 92 95Ч97 119 122 125Ч126 149 150 159 165 172 179 197 204 264
Delaunay, B.      258
Determinant      68 78 155 236 268 290Ч291 294 296 see "Forms" "Ternary"
Dickson, L.E.      47 95 183Ч184 214 247Ч248 251 268 283 287Ч292 293-301
Diophantus      60
Dirichlet series      97 128Ч129 138Ч140 147Ч148 157 165 188 192
Dirichlet, G.L.      1 13 16Ч21 24Ч29 31 35 36 38 40 41 44 51 60 66 68 77 81 83Ч87 92 95 97Ч105 107 109 111 115 117Ч119 122 124 129 136Ч140 146Ч148 150Ч151 153Ч154 156Ч159 162 164Ч167 169Ч170 172Ч175 178Ч179 181Ч182 188 192 195 198Ч200 203Ч206 210 212 222 224 229 242 250 265 273 275
Divisors, functions of      23 29 108Ч109 115 122 128 130Ч131 136 142 176Ч177 180Ч181 186 189 193 196
d|m      168
E(D)=fundamental unit      138
Eisenstein, G.      34 57 59 80 88 103 204 206 210 211 213Ч217 222Ч223 225 228 234 236 238 241 253Ч254 258 259 261Ч263 284
Elementary chord      42
Elementary divisor      285
Elementary triangle      42 167
Elliptic function      20 105 106 108Ч109 113 121 134 136 162 185Ч186 204
Elliptic function, complex multiplication of      105 120 151
Elliptic modular function      32 36 125Ч128 130Ч131 140Ч141 148 150 197
Elliptic modulus      94 105Ч111 120 126
Epstein, P.      53
Equivalent numbers      32 44 53
Equivalent numbers, relatively      128 140Ч141
Erler, H.W.      64 103Ч104
Euler's constant      45 84 146 164 184
Euler, L.      1 3Ч5 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      1Ч3 8 15 206
Fields, J.C.      39
Fontene, G.      48
Form problem      296
Forms never $\equiv 0 (mod \ p)$      292
1 2 3
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