Berndt B.C., Evans R.J., Williams K.S. — Gauss and Jacobi Sums :: Электронная библиотека попечительского совета мехмата МГУ

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Berndt B.C., Evans R.J., Williams K.S. — Gauss and Jacobi Sums

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Название: Gauss and Jacobi Sums

Авторы: Berndt B.C., Evans R.J., Williams K.S.

Аннотация:

Devised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories. Though the main focus is on Gauss and Jacobi, the book does explore other relevant formulas, including Cauchy.

Язык:

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 600

Добавлена в каталог: 21.05.2005

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

Предметный указатель

Exponential sum      387
f-nomial period      see “Period”
Fabrykowski, J.      210
Farsi, C.      3 51—52 54
Fermat equation      490
Fermat's last theorem      468 492
Fermat's little theorem      234
Fermat, P.      2
Finite field      5 7 234
Finite Fourier transform      47 51—52 386
Fisher, B.      386
Fourier coefficients      211 292
Fourier series      98 365
Fourier transform      51—52 386
Frame, J.S.      53
Fredricksen, H.      150 152 181
Frei, G.      495
Fricke, R.      171
Friesen, C.      152 233 265 267
Frobeuius automorphism      387
Froeberg, C.-E.      160
Froehlich, A.      55 494—495
Fulton, J.      340
Funakura, T.      3 31 53—54
Function field      53 55 495
Functional equation      2
Fundamental unit      99
Furtado Gomide, E.      337
Furtwaengler, P.      494
Furuta, Y.      267
Gao, S.      339
Gathen J. von zur      339
Gauss      1—2 50 97 99
Gauss period      see “Period f-nomial”
Gauss sum      9 11—12 29 50 153 171 181 212 342 439
Gauss sum applications to difference sets      175
Gauss sum applications to residuacity      212
Gauss sum of order 12      166
Gauss sum relationship with Eisenstein sums      421
Gauss sum relationship with Jacobi sums      59 02 301
Gauss sum relationship with periods      327 332 426
Gauss sum, biquadratic      160 163 171 424 496
Gauss sum, cubic      3 154—160 422
Gauss sum, double      56
Gauss sum, Galois      2 55
Gauss sum, generalised      13
Gauss sum, half      55
Gauss sum, incomplete      55 496—497
Gauss sum, lift of      358 385
Gauss sum, multiplicative property of      15
Gauss sum, ortic      164 172
Gauss sum, pare      1 342 362—363 385
Gauss sum, partial      55 496—497
Gauss sum, prime ideal factorization of      96 346—348 384 387
Gauss sum, primitive      53 55
Gauss sum, product identities for      388
Gauss sum, quadratic      1 12 25 50 52—55 362 383—385 422
Gauss sum, quartic      160 163 171 424 496
Gauss sum, quintic      172
Gauss sum, reciprocity theorems for      13 52—53 493—196
Gauss sum, relative      4 439
Gauss sum, relative norm of      387
Gauss sum, sextic      154 171
Gauss sum, symplectic      253
Gauss' diary      1 50
Gauss' evaluation of a quadratic Gauss sum      18
Gauss, C.F.      1—2 50 53 71 97—99 151 171 210 231 265—266 268 291 337 338
Gaussian integer      241
Gaussian integer primary      242
Gaussian integer prime      65 241
Gaussian polynomial      18 20 50—51
Gaussian prime      65 241
Genocchi, A.      51—52 210
Gerardin, P.      55
Gerth, F.III.      55
Giudici, R.E.      151 438 466—467
Glaisher      330
Glaisher, J.W.L.      339
Glashan, J.C.      338
Goldberg, J.      55
Goldscheider, F.      232
Goldstine, H.H.      159
Gordon, D.      174
Gosset, T.      231 263
Gould, H.W.      442
Gouvea, F.Q.      63 385
Grant, D.      266
Granville, A.      292—293 337
Gras, G.      384—385
Grass      1
Gray, J.      50
Greene, J.      5 385 387 453
Gross — Koblitz formula      2 4 268 276—278 350 387
Gross, B.      1 2 4 350
Grosswald, E.      50
Guinand, A.P.      51
Gurak, S.J.      387 427 439
Guy, R.K.      482
Gyoja, A.      55 336
Habicht, W.      265
Hadamard matrix      439
Hadano, T.      497
Haiberstadt, E.      54
Hall, M.Jr.      174
Halter-Koch, F.      232
Han, W.B.      388
Hannay, J.H.      3 54
Hardy, K.      68 143 171 267 438
Hasse      1
Hasse, H.      1 4 51—53 97 99 151 171 209 232—233 267 384—385 494—495
Hayashi, Harry S.      337
Hayashi, Heima      265
Hayes, D.R.      495
Heath-Brown, D.R.      160
Hecke character      387 495
Hecke, E.      51—52 54 387
Helou, C.      267 495
Helversen-Pasotto, A.      55
Hermite polynomial      54
Hilbert symbol      494
Hilbert's reciprocity law      494
Hilbert, D.      494
Hill, J.R.      152 229
Hiramatsu, T.      267
Hopf, H.      210
Howe, L.J.      233
Hua, L.-K.      50 52—55 336—337
Huard, J.G.      151 293 384 497
Hudson, R.H.      99 195 209—210 231—233 291—293
Hull, R.      336
Hurt, N.      387
Hurwitz, A.      336
Husemoller, D.      55 495
Hwang, F.K.      99
Hypergeometric character sum      173 385 387 4671
Ihara, Y.      63 388
Index of an integer with respect to a primitive root g      66 81; reciprocity“
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g k \ \left(\mod k \ \right)$       83—84 498
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g l \ \left(\mod k \ \right)$       87 80
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g q \ \left(\mod q^k \ \right)$       232
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g-3$       216
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g11$       215
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g2$       81—83 90 99 102 134—135 151 213 221 225 230 233 262 336
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g3$       86 90—91 99 102 115 120 213 216 218 221—222 231—232
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g5$       86 94 102 133 136 213—214 217 220 222 233
Index of an integer with respect to a primitive root g, $\mathrm{ind}_g7$       214 223 230 233
Integral basis      111 113 120 138 140 388
Ireland, K.      5—8 62 97 234 240—241 251 265 336 385 494 495
Irreducible cyclic code      342 369 383 386 439
Ishibashi, H.      3 151 293 387

Ishii, N.      267
Ishikawa, T.      292 339
Ismoilov, D.      173
Ito, H.      164
Iwaniec, H.      386
Iwasawa, K.      63 97 388
jacobi      1—2
Jacobi sum      57 97 100 150
Jacobi sum of order 10 (decic)      124 150—151
Jacobi sum of order 11      148
Jacobi sum of order 12 (duodecic)      115 150—151
Jacobi sum of order 13      148 151
Jacobi sum of order 14      150 152
Jacobi sum of order 15      148 150
Jacobi sum of order 16 (bioctic)      111 150—151
Jacobi sum of order 18      150
Jacobi sum of order 2 (quadratic)      150
Jacobi sum of order 20 (bidecic)      136 151
Jacobi sum of order 21      149 151
Jacobi sum of order 22      150—151
Jacobi sum of order 24 (biduodeetc)      118 150—151
Jacobi sum of order 28      151
Jacobi sum of order 3 (cubic)      103 106 150—151 237 435 473
Jacobi sum of order 30      150
Jacobi sum of order 32      496
Jacobi sum of order 39      149 151
Jacobi sum of order 4 (quartic)      107—108 150—151 243 435
Jacobi sum of order 40      149
Jacobi sum of order 5 (quintic)      124 150—151
Jacobi sum of order 55      151
Jacobi sum of order 56      151
Jacobi sum of order 6 (sextic)      103 107 150—151
Jacobi sum of order 60      149 151
Jacobi sum of order 7 (septic)      140 147 151—152
Jacobi sum of order 8 (octic)      109 150—151 471
Jacobi sum of order 9      148 150—151
Jacobi sum relationship with binomial coefficients      268 270 336
Jacobi sum relationship with cyclotomic numbers      70 95 98 365
Jacobi sum relationship with Gauss sums      59 92 301
Jacobi sum relationship with Jacobsthal sums      188
Jacobi sum relationship with p-adic gamma functions      278
Jacobi sum, congruence for      60—61 63 66 97—98
Jacobi sum, degree over Q      336
Jacobi sum, generalized      4 295—296 336
Jacobi sum, generalized, reduction formula for      298
Jacobi sum, generalized, relationship with Gauss sums      301
Jacobi sum, lifted      361—362 382
Jacobi sum, order of      57
Jacobi sum, primality test      07
Jacobi sum, prime ideal factorization      66 98 336 346 384
Jacobi sum, pure      342 302—363 385—386
Jacobi sum, reciprocity law for      495
Jacobi symbol      17
Jacobi, C.G.J.      1—2 97—99 150—151 171 211 231 264—265 291—292 384 468 494
Jacobsthal sum      84 209 211
Jacobsthal sum application to quadratic residues      106
Jacobsthal sum of order 10      193 209
Jacobsthal sum of order 12      194 209 497
Jacobsthal sum of order 16      497
Jacobsthal sum of order 2      190 195 200
Jacobsthal sum of order 24      497
Jacobsthal sum of order 3      190 196 200 209
Jacobsthal sum of order 4      190—191 209
Jacobsthal sum of order 5      191 209
Jacobsthal sum of order 6      192 209
Jacobsthal sum of order 8      102
Jacobsthal sum of order 9      209
Jacobsthal sum of prime order      209
Jacobsthal sum relationship with Jacobi sums      188
Jacobsthal sum, congruence for      190
Jacobsthal sum, double      202—205 208
Jacobsthal sum, orthogonality relation of      187
Jacobsthal sum, properties of      184
Jacobsthal, E.      3 97 195 209—210
Jager, H.      53
Jakubec, S.      98 232 339 384
Joly, J.-R.      97 339
Jordan, C.      337
Joris, H.      53
Joux, A.      183 210
Jungnickel, D.      3 174 182 385 438—439
Kaplan, P.      53 266 337
Karatsuba, A.      210
Katre, S.A.      98 152 209 211 233
Katz      1
Katz, N.M.      1 173 386
Kawanaka, N.      55
Kesava Menon, P.      55
Kida, M.      336
Kim, D.S.      55
Klein, S.      3 54 573
Kloosterman sum      3 383 380 387
Kloosterman, H.D.      386
Kmummer      1 204 387 494
Knuth, D.E.      101
Koblitz      1
Koblitz, N.      1—4 29 31 34 37 336—337 340 349—350 387
Koike, M.      467
Kolyvagin      388
Kondo, T.      55
Konyagin, S.V.      172 339
Korobov, N.M.      172 210
Koschmieder, L.      265
Kraezer, A.      52
Kratsel, E.      171
kronecker      1
Kronecker symbol      54
Kronecker — Weber Theorem      388
Kronecker, L.      1 51—52 54 98
Kuang, J.H.      4 400
Kubert, D.S.      387—388
Kubota, T.      160
Kummer sum      3 159 171
Kummer — Lehmer residuacity criterion      339
Kummer's conjecture      139
Kummer's reciprocity law      200
Kummer, E.E.      1 97—98 159 171 173 264 266 338—339 384 439 468 494
l-adic expansion of Gauss and Jacobi sums      388
L-function      29 54 266 377
L-function, functional equation      266
L-function, root number      206
Lachaud, G.      386
Lahtonen, J.      387
Lakkis, K.      388
Lam, T.Y.      340
Lamprecht, E.      55
Landau, E.      51—54 494
Landsberg, G.      52
Lang, S.      337 350 384—385
Langevin, P.      3 386 439
Laws of reciprocity      see “Reciprocity laws”
Lazarus, A.J.      338
Lebesgue, V.-A.      53—54 97 99 171 326 331 337—338
Legendre symbol      66
Legendre, A.-M.      338
Lehmer, D.H.      1 55 99 151 171 182 203 211 338—339 496
Lehmer, E.      1 6 99 151—152 160 164 171—172 179 181 182 195 203 209 211 231—233 266—267 291 338—339
Leichtle, C.      3 54
Lemmermeyer, F.      53 99 249 267 495
Lenstra, A.K.      97
Lenstra, H.W.      97
Leonard, P.A.      63 151—152 209 232 267 466
Leprevost, F.      210 387 466
Lerch, M.      52 54
Leung, K.H.      340
Li, B.-H.      54
Li, S.      337
Li, T.-J.      54
Li, W.-C.      55 387
Libri, G.      99 326 338

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