 17 57
Abelian L-function 5 164ff 182
Absolute value 20ff
Additive approximation theorem 38
Adeles 32ff
Admissible subgroup 192
Algebraic number field 9
Analytic continuation 139 154 159
Approximation theorem 29 38 45
Archimedian valuation 20
Arithmetic progression 197 236
Artin character 182 227
Artin reciprocity law 5 166 171 182 183 186
Artin symbol 169
Bauer's Theorem 164 208
CHARACTER 111
Chinese remainder theorem 18
Class field 230 234
Class field theory 181ff
Class group 192
Class number 42 172
Class number formula 172
Completion 22 55
Conductor 118 156 206 215
Conductor-discriminant formula 183
Congruences 17 38
Critical strip 34
Cyclic extension 190
Cyclotomic field 4 96ff 238
Decomposed prime 74
Decomposition subfield 87
Decomposition theorem 235
Dedekind zeta function 158
Defining modulus 192
Different 65 80
Dirichlet density 163
Dirichlet L-series 3 4 171
Dirichlet's theorem 167
Discriminant 12 67 80 81 100 101
Discriminant, of basis 11 58
Dual group 111
Dual group of additive group of local field 114
Dual group of adele ring 120
Dual group of finite group 113
Dual group of multiplicative group of local field 116
Dual group of restricted direct product 118
Duality 111
Entire function 259 265
Euler product 3 145 158
Existence theorem 230
Field polynomial 10
First inequality 197
Fourier inversion theorem 121 128
Fourier transform 121
Fractional ideal 14
Frobenius automorphism 69 84ff 102 164
Functional equation 139 154 159
Fundamental domain 152
Fundamental unit 45
Galois correspondence 217 225
Gamma function 258
Gaussian sum 145 175
Generalized conductor 157 183 192
Generalized discriminant 183
Global class field theory 226ff
Global zeta function 145ff
Greatest common divisor 17
Groessencharacter 145 175 194 227
Groessencharacter of classical type 194
Hadamard's lemma 263
Hecke character 157 195
Hecke L-series 133 156ff
Hensel's lemma 49
Herbrand's lemma 189 232
Herbrand's unit theorem 198ff
Hilbert theory 67 84
Hilbert's reciprocity law 215
Hilbert's Satz 90 188 202
Ideal 12ff
Ideal character 157
Ideal class 257
Ideal mapping 151
Idele class character 145
Ideles 33 38ff
| Imaginary quadratic field 12
Inert prime 74
Inertia group 68
Inertia subfield 87
INTEGER 9ff
Integral basis 12
Invariant differential operator 128
Kronecker symbol 88
Kronecker's theorem 96 238ff
Kummer's theorem 78
Legendre symbol 172
Local field 32 46ff
Local norm 220
Local norm index 220
Local uniformizing parameter 26 56
Local zeta function 133ff
Locally constant function 129
Minimal basis 12
Minimal polynomial 10
Modulus 28
Modulus of automorphism 36 37
Multiplicative approximation theorem 45
Natural density 252
Norm 52 77
Norm of ideal 29 72
Norm residue symbol 184 215 218 223 227 242
Phragmen — Lindeloef theorem 258
Poisson summation formula 148
Pontryagin duality 112
Power reciprocity law 241ff
Power residue symbol 243
Prime 28 56
Prime ideal theorem 252 256
Prime number theorem 2 254 271
Prime, complex 28
Prime, finite 28
Prime, infinite 28
Prime, real 28
Primes in arithmetic progressions 3 4 168
Primitive character 157
Product formula 36
Quadratic field 88
Quadratic reciprocity law 106—107
Ramification groups 70 86
Ramification index 56 62ff
Ramified extension 56 62ff
Ramified prime 81
Real quadratic field 12
Reciprocity law 5 106—107 228
Regulator 152
Relatively prime ideals 17
Residue class degree 60 73
Residue class field 30
Restricted direct product 32
Riemann hypothesis 3 255 272 282
Riemann zeta function 2
Schwartz — Bruhat function 146
Schwartz — Bruhat space 127ff
Second inequality 188
Self-dual measure 121ff
Splitting type 162 236
Strong reciprocity law 216—217
Supplementary reciprocity law 247
Tame ramification 71 88
Tate's thesis 133
Tchebotarev density theorem 168ff
Topological field 21
Totally disconnected 26 27
Trace 52 77
Undecomposed prime 162
Uniqueness theorem 230
Unit theorem 43
Valuation 20ff 54 79
Valuation, archimedean 20 49 50 51
Valuation, complex 24
Valuation, equivalence of 22
Valuation, finite 20
Valuation, infinite 20
Valuation, non-archimedean 20 21 24
Valuation, real 24
Vandermonde determinant 11 66 100
Volume of an idele 39
Weak reciprocity law 207ff
Weierstrass canonical product 259 266
Wild ramification 71
|
|
|
О проекте