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| Eichler M. — Introduction to the Theory of Algebraic Numbers and Functions |
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| Предметный указатель |
Abel's theorem 199 209
Abelian integral 213
Abelian variety see "Variety"
Addition theorem 192 198 211
Antiautomorphism see "Rosati adjoint"
Artin, E. 314 315
Associative law 240
Base units see "Unit"
Basis 5
Basis, Complementary 10
Basis, theorem 5 13
Behnke, H. 141(2) 142
Berger, R. 79
Bounded ramification see "Ramification"
Canonical class see "Class"
Canonical system of incisions 189
Cartier operator 150ff
Cartier, P. 151
Cassels, J.W.S. 204
CHARACTER 219 275
Chevalley, C. 135 142 151(3)
Class, canonical 133ff 156ff
Class, differential 156ff
Class, divisor 22ff 80 120ff 179
Class, ideal 54 98
Class, principal 133
Complement 73ff
Complementary basis see "Basis"
Complementary module see "Module"
Component 21 67ff 88ff 128ff
Conforto, C. 204
Congruence subgroup 217ff
Conservative 157 174
Content 60
Convergence radius 110
Correspondence 233ff
Correspondence in extended sense 285ff
Correspondence, Frobenius 249 306
Correspondence, inseparable 246ff
Correspondence, modular 266ff 308ff
Correspondence, prime 245
Courant, R. 202
Cusp 217
Cusp, form 228 271ff
Davenport, H. 314 315
Decomposition group 104
Degree of a correspondence 235
Degree of a divisor 80 85 89 120 124 130
Degree of a linear divisor 23 89 130
Deuring, M. 114 174 184 200 202 244 266 314 315 319
Diagonal 167
Different 75ff see
Differential 147ff 158 223 252
Differential, class see "Class"
Differential, exact 151
Differential, kind 155
Differential, quotient 143
DIMENSION 5 23 132
Dirichlet see "Unit theorem"
Discriminant 29 75ff 96ff 228 278
Discriminant, theorem 77
Distortion ratio 263
Divisor 79ff 120ff 128ff see
Divisor of a differential 147 158ff
Divisor of fixed points 283 286ff
Divisor, diagonal 167
Divisor, different 89 128
Divisor, integral 121
Divisor, Kronecker 57 87
Divisor, linear 22 88 128
Divisor, principal 57 80 82 120ff
Divisor, system, nonspecialized 294
Divisor, unit 79 120
Dual space 10 128
Eichler, M. 19 231(2) 232 265 278(3) 280(4 4a) 281 314(4) 315
Eisenstein series 220 225
Elementary divisor theorem 7
Equivalence of correspondences 235 244 285
Equivalence of divisors 84 88 120 129
Equivalence of principal part systems 160
Equivalence, quasi 62
Falb, P. 157
Field of constants 1
Field of definition 133
Field of elliptic functions 190ff 315ff
Field, cyclotomic 106
Field, decomposition 106
Field, extension of 135ff
Field, inertial 91
Field, quadratic number 104
Finiteness criteria 7 12
Fixed points 260ff 282ff
Fixed points, number of 289
Fixed points, theorem 264
Frobenius see "Correspondence"
Fueter, R. 228
Fundamental domain 39
Gauss sums 44ff
Generators, system of 6
Genus 133ff 188
Genus, relative 134
Genus, topological 188
Green's function 165ff
Grothendieck, A. 298 299
Hasse, H. 79 98 99 101 151 184 203 204 314 315
Hecke, E. 98 231 278(6) 279 280 281
Herglotz, G. 307
Hofmann, J.E. 204
Holomorph 220
Hua, L.K. 41
Hurwitz genus formula 135
Hurwitz, A. 202 242 266
Hyperbolic plane 36
Hyperbolic space 36
Ideal 5ff 53ff see "Norm"
Ideal, extension of 70
Ideal, integral 54
Ideal, prime 58 72
Ideal, prime, conjugate 91
Ideal, prime, regular 174
Igusa, J.I. 184 203 204 278
Inertia theorem 173
Inertial group 91
Inseparable extension 30 54 see
Integral(s) of first kind 196ff 204ff
Integral(s) of third kind 208ff
Integral(s), dependence 53
Invariance 86 135
Invariance, projective 81
Jacobian variety see "Variety"
Kappus, H. 171 265
Klinger, H. 41
Knopp, K. 202
| Kuga, M. 214
Kunz, E. 79 157
Lamprecht, E. 31 183 184
Lang, S. 204 213(1 2) 214
Lattice point theorem 14ff
Legendre relation 206
Legendre relation, symbol 44ff
Lemniscatic 204
Level 217
Linear divisor see "Divisor"
Local ring 63ff
Local theory 3
Local uniformizers 187 214ff
Manifold 186ff
Mattuck, A. 183(7) 184 298 299
Meromorph 186 220
Meromorphism 316
Meyer, C. 99
Model 83 86 131
Modular correspondence see "Correspondence"
Modular form 219ff 275ff
Modular function 43 220ff 266ff
Modular surface 214
Modular triangle 40 214ff
Module, complementary 10 22
Mordell, L.J. 203 204
Multiple 23 232
Multiplier 43 132
Nastold, H.J. 157
Nering, E.D. 184
Neron, A. 213(2) 214
Noetherian ring 11ff 61
Norm of divisors 85 124
Norm of ideals 70 93
Norm of linear divisors 23
Norm, absolute 300
Normal form see "Weierstrass"
Normed 275
Order function 79ff 120ff 147ff 158
Order of a fixed point 265
p-component 21 67
p-constant 146
p-variable 146
Period 197 204ff 257
Period, matrix 204
Period, relation 204
Petersson, H. 171 231(4 6) 232 278 281
Pfetzer, W. 232
Place 20ff 64 79ff 120ff
Place, critical 114ff
Place, regular 114ff
Pole 110 148
Power series 110ff 133
Prime correspondence see "Correspondence"
Prime element 64 112 124 147
primitive 221
Principal part system 160
Product of correspondences 236ff
Product of rings 234
Product, scalar, of principal part systems 160
Product, scalar, Petersson 273ff
Pseudocomplement 73ff 89
Pseudodifferent 75
Pseudodifferent, divisor 89
Pseudodiscriminant 30 75
Pseudotrace 30
Ramification 93 216ff
Ramification, bounded 253 271
Ramification, field 95
Ramification, group 94ff
Ramification, index 72 84 95
Ramification, irregular 95
Ramification, number 72 84 95
Ramification, regular 95
Rangachari, S.S. 315
Reciprocity law 47 139
Reflection automorphism 193ff
Regulator 104
Reiner, J. 41
Residue 151ff
Residue, class degree 72
Residue, theorem 153
Riemann surface 185
Riemann — Roch theorem 26 133ff 141
Roquette, P. 141 142 184 298 299
Rosati adjoint 241 259
Rosenlicht, M. 142
Saferevic, I.R. 190
Samuel, P. 91 95
Schiffer, M. 141(2) 142
Schmidt, F.K. 142 314 315
Schoeneberg, B. 232
Separable 30 131 143 149ff
Separating element 143
Serre, J.-P. 298
Shimura, G. 214 278 281 313 319
Siegel, C.L. 41 43 206
Sommer, F. 141(2) 142
Spencer, D.C. 141(1) 142
Subdegree 117
Symplectic, group 32ff 205
Symplectic, matrix 32 205
Symplectic, modular form 42
Symplectic, modular group 36
System of generators 6
Tamagawa, T. 142
Taniyama, Y. 315 319
Tate, J. 135 298 299
Teichmueller, O. 171
Theta function 41ff 44ff 232
Trace 27ff 122 259ff 283 291
Trace, formula 263
Transitivity formula 27 72
Translation automorphism 193ff
Tricomi, F. 203 204
Unimodular 7
UNIT 5 83
Unit, base 101 105
Unit, divisor see "Divisor"
Unit, theorem 101
Vahlen, K.Th. 36
Van der Blij 278 281
Van der Waerden, B.L. 63 142
Variety, abelian 214
Variety, Jacobian 211ff
Weierstrass normal form 200
Weil, A. 141(11) 142 204 298 299 314 315
Weyl, H. 141(12) 142
Witt, E. 38 142
Wohlfahrt, K. 280 281
Zariski, O. 91 95 157
Zero 110 148
Zeta function 299ff
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