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.

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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

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Предметный указатель

Abe, M.      387
Abel-Plana summation formula      51
Acharya, V.V.      98 152 209 211
Adleman, L.      97
Adolphson, A.      387
Agrawal, M.K.      99 210 232 292 497
Aigner, A.      99 231—232 267
Airy integral      386
Akiyama, S.      385—386
Aladov, N.      210
Alderson, H.P.      99 232
Andrews, G.E.      51 209 385
Ankeny, N.C.      99 232
Aoki, N.      336
Apery number      467
Apostol, T.M.      8 29 52
Artin's reciprocity law      494 495
Artin, E.      494
Askey, R.      385
Auslander, L.      52
Autocorrelation      439
Automorphism      26
Automorphism, Frobenius      387
Autuore, J.      385
Averbukh, I.SH.      3 54
Ayoub, R.      8 51
Babaev, G.      173
Bach, E.      339
Bachmann, P.      97 171 338
Bailey, D.      293
Bambah, R.P.      52
Barkan, P.      164
Barrucand, P.      50 231
Basse's conjecture      385
Baumert, L.D.      3 150 152 174 179 181—182 385 439
Beeger, N.G.W.H.      232 482
Bellman, R.      52
Benkoe, I.      51
Berndt      6
Berndt, B.C.      6 51—52 54—56 98 151 169 171—172 181 195 209 211 338 377 387 396 438—439 465—467 496—497
Berry, M.V.      3 54—55
Bessel function      386
Beukers      293
Beukers, F.      293
Beyer, G.      160
Bickmore, C.E.      231—233
Binomial coefficients      18 268
Binomial coefficients, Cauchy — Whiteman congruences for      292
Binomial coefficients, congruences (mod ) for      211 268 280—286290 293 498
Binomial coefficients, congruences (mod p) for      200—202 211 268—274 288—292 417—419 435 437
Binomial coefficients, relationship with Jacob sums      66 268 279 6
Bochner, S.      52
Bombieri, E.      183
Borevich, Z.      53—54
Boyarsky, M.      388
Brauer, A.      210
Bremser, P.S.      55
Bressoud, D.M.      51
Brewer sum      5 440
Brewer sum, generalized      440 458 466
Brewer sum, generalized, $\Lambda_{10}(\alpha)$       464 464
Brewer sum, generalized, $\Lambda_{12}(\alpha)$       464 466
Brewer sum, generalized, $\Lambda_{14}(\alpha)$       466
Brewer sum, generalized, $\Lambda_{18}(\alpha)$       466
Brewer sum, generalized, $\Lambda_{1}(\alpha)$       460
Brewer sum, generalized, $\Lambda_{2}(\alpha)$       461
Brewer sum, generalized, $\Lambda_{3}(\alpha)$       461
Brewer sum, generalized, $\Lambda_{4}(\alpha)$       463
Brewer sum, generalized, $\Lambda_{5}(\alpha)$       464—466
Brewer sum, generalized, $\Lambda_{6}(\alpha)$       463 466
Brewer sum, generalized, $\Lambda_{7}(\alpha)$       466
Brewer sum, generalized, $\Lambda_{8}(\alpha)$       464 466
Brewer sum, generalized, $\Lambda_{9}(\alpha)$       466
Brewer sum, generalized, $\Lambda_{n}(\alpha)$ , $\Lambda_{2n}(\alpha)$       440 458—459 466
Brewer sum, generalized, relationship with Jacobsthal and Eisenstein sums      459
Brewer sum, ordinary      440 443 466
Brewer sum, ordinary, $\Lambda_{10}(\alpha)$       456
Brewer sum, ordinary, $\Lambda_{1}(\alpha)$       450
Brewer sum, ordinary, $\Lambda_{2}(\alpha)$       450
Brewer sum, ordinary, $\Lambda_{3}(\alpha)$       450—451 466
Brewer sum, ordinary, $\Lambda_{4}(\alpha)$       452 466
Brewer sum, ordinary, $\Lambda_{5}(\alpha)$       454 465—466
Brewer sum, ordinary, $\Lambda_{6}(\alpha)$       453
Brewer sum, ordinary, $\Lambda_{8}(\alpha)$       457 467
Brewer sum, ordinary, $\Lambda_{n}(\alpha)$ , $\Lambda_{2n}(\alpha)$       440 444—445 447 450 453 456 458 466
Brewer sum, ordinary, relationship with Jacobsthal and Eisenstein sums      445 450
Brewer, B.W.      3 5 53 211 440 466—467
Brillhart, J.      249
Brinkhuis, J.      384 387—388
Bruckner, H.      494
Bruedern, J.      340
Brumei — Stark element      495
Brumer — Stark conjecture      387
Buck, N.      152
Buell, D.A.      210 292
Burde, K.      209—211 232 266—267 498
Burgess, D.A.      5 55
Burnside, W.      338
Bushnell, C.      55
Caragiu, M.      210
Carey, F.S.      338
Carlitz      1
Carlitz, L.      1 51—52 54 336 340 384—387
Cassels, J.W.S.      158—160 494—495
Cauchy      1
Cauchy, A.      1 51 97 291—292
Cayley, A.      338
Chalk      6
Chalk, J.H.H.      6
Chandrasekharan, K.      52
CHARACTER      9 28
Character sum      28 58 173 183 198 206—208 210 385 387 400 449 453 467;
Character, biquadratic      241
Character, conductor of      28 45 380 387 495
Character, cubit      235
Character, Dinchlet      28 379
Character, Hecke      387 495
Character, k-power residue      see “Power residue symbol”
Character, lift of      342 356 385
Character, primitive      29 45 49—50 53—54
Character, quadratic      12 29 54 379 382
Character, quart it      241
Character, restriction of      355
Character, trivial      9
Chowla      1
Chowla — Mordell theorem      53
Chowla, I.      336
Chowla, P.      466
Chowla, S.      1—2 31 52—54 171—172 181 209—211 231 268 293 336 338 340 386
Chung, F.R.K.      387
Class number      54 164 377
Coates, J.H.      384
Code word      368—369;see also “Weight”
Cohen, E.      337
Cohen, H.      97
Cohen, S.D.      98 174 211
Cohn, H.      231
Coleman, R.F.      350 3&8
Collison, M.J.      264
Congruences      see also “Diagonal equations”
Congruences, Cauchy — Whiteman type      292
Congruences, Cauchy — Whiteman type, $A_1 x_1^3 + A_2 x_2^3 \equiv A \ \left(\mod p \ \right)$       310 321 324—325 327
Congruences, Cauchy — Whiteman type, $A_1 x_1^3 + \cdots + A_n x_n^3 \equiv A \ \left(\mod p \ \right)$       307 337
Congruences, Cauchy — Whiteman type, $A_1 x_1^4 + A_2 x_2^4 \equiv A \ \left(\mod p \ \right)$       317 321 333 337
Congruences, Cauchy — Whiteman type, $A_1 x_1^4 + \cdots + A_n x_n^4 \equiv A \ \left(\mod p \ \right)$       314—315
Congruences, Cauchy — Whiteman type, $A_1 x_1^5 + \cdots + A_n x_n^5 \equiv A \ \left(\mod p \ \right)$       337
Congruences, Cauchy — Whiteman type, $A_1 x_1^k + \cdots + A_n x_n^k \equiv 0 \ \left(\mod p \ \right)$       331
Congruences, Cauchy — Whiteman type, $A_1 x_1^k + \cdots + A_n x_n^k \equiv A \ \left(\mod p \ \right)$       320—321
Congruences, Cauchy — Whiteman type, $A_1 x_1^{k_1} + \cdots + A_n x_n^{k_n} \equiv 0 \ \left(\mod p^s \ \right)$       340
Congruences, Cauchy — Whiteman type, $A_1 x_1^{k_1} + \cdots + A_n x_n^{k_n} \equiv A \ \left(\mod p \ \right)$       294—295

Congruences, Cauchy — Whiteman type, $A_1 x_1^{m_1} + A_2 x_2^{m_2} \equiv A \ \left(\mod p \ \right)$       320—321
Congruences, Cauchy — Whiteman type, $x^3 + y^3 + 2z^3 \equiv 0 \ \left(\mod p \ \right)$       334
Congruences, Cauchy — Whiteman type, $x_1^2 + \cdots +x_r^2 \equiv 0 \ \left(\mod p^n \ \right)$       46
Congruences, Cauchy — Whiteman type, $x_1^2 + \cdots +x_{p'}^2 \equiv p' \ \left(\mod p \ \right)$       306
Congruences, Cauchy — Whiteman type, $x_1^3 + x_2^3 + x_3^3 \equiv 1 \ \left(\mod p \ \right)$       2 325
Congruences, Cauchy — Whiteman type, $x_1^3 + x_2^3 \equiv 1 \ \left(\mod p \ \right)$       323
Congruences, Cauchy — Whiteman type, $x_1^3 + x_2^3 \equiv A \ \left(\mod p \ \right)$       310
Congruences, Cauchy — Whiteman type, $x_1^3 + \cdots +x_n^3 \equiv 0 \ \left(\mod p \ \right)$       313 335
Congruences, Cauchy — Whiteman type, $x_1^3 + \cdots +x_n^3 \equiv A \ \left(\mod p \ \right)$       312
Congruences, Cauchy — Whiteman type, $x_1^4 + x_2^4 \equiv 1 \ \left(\mod p \ \right)$       323
Congruences, Cauchy — Whiteman type, $x_1^4 + x_2^4 \equiv A \ \left(\mod p \ \right)$       317 335
Congruences, Cauchy — Whiteman type, $x_1^4 + \cdots +x_n^4 \equiv 0 \ \left(\mod p \ \right)$       332
Congruences, Cauchy — Whiteman type, $x_1^4 + \cdots +x_q^4 \equiv q \ \left(\mod p \ \right)$       337
Congruences, Cauchy — Whiteman type, $x_1^5 + x_2^5 \equiv 1 \ \left(\mod p \ \right)$       323
Congruences, Cauchy — Whiteman type, $x_1^k + x_2^k \equiv 1 \ \left(\mod p \ \right)$       322
Congruences, Cauchy — Whiteman type, $x_1^k + \cdots +x_n^k \equiv 0 \ \left(\mod p \ \right)$       339
Congruences, Cauchy — Whiteman type, $x_1^k + \cdots +x_s^k \equiv y \ \left(\mod p \ \right)$       339
Conrad, K.      293 384
Continued fraction      164
Cooke, G.      265—266 494
Corson, H.H.      341
Coster, M.J.      293
Cowles, J.      338 340
Cowles, M.      338 340
Cox, D.A.      53 157 494—495
Crandall, R.      4 164 284 482
Cunningham      99
Cunningham, A.      99 231—232
Curtis, C.W.      385—386
Cyclic code      368
Cyclotomic field      26
Cyclotomic matrix      68
Cyclotomic matrix of older 8      95
Cyclotomic matrix of order 2      70
Cyclotomic matrix of order 3      70
Cyclotomic matrix of order 4      70
Cyclotomic matrix of order 5      93
Cyclotomic matrix of order 6      94
Cyclotomic matrix of order 7      95
Cyclotomic number      3 4 68 81 98—99 181—182 365
Cyclotomic number of of order 12      152
Cyclotomic number of of order 14      152
Cyclotomic number of of order 15      152
Cyclotomic number of of order 16      152 229
Cyclotomic number of of order 18      152
Cyclotomic number of of order 20      152
Cyclotomic number of of order 24      152
Cyclotomic number of of order 32      496
Cyclotomic number of order 10      152
Cyclotomic number of order 11      152
Cyclotomic number of order 2      69 80—81 152
Cyclotomic number of order 3      70—71 74 149 152
Cyclotomic number of order 4      70 74 78 149 152
Cyclotomic number of order 5      93—94 99 149 152
Cyclotomic number of order 6      94 149 152
Cyclotomic number of order 7      149 152
Cyclotomic number of order 8      149 152
Cyclotomic number of order 9      152
Cyclotomic number relationship with f-normal periods      328—329 437—438
Cyclotomic number relationship with Jacobi sums      79 95 98 365
Cyclotomic number, generalized      87 322
Cyclotomic period      see “Period f-normal”
Cyclotomic polynomial      62
Dabrowski, R.      387
Dantscher, V.      265
Darmon, H.      338
Davenport      1
Davenport — Haase product formula      4 59 342 351 355 384—386 497
Davenport — Hasse theorem on lifted Gauss sums      4 342 358 360 392 492
Davenport, H.      1 4 50—51 53 209—210 384—385
Davis, K.      293
Desarmenien, J.      293
Deuring's theorem      210
Deuring, M.      210
Diagonal equations      3—4 294 336 340;
Diagonal equations,       338
Diagonal equations, $A_1 x_1^k + \cdots + A_n x_n^k = A$       340 437
Diagonal equations, $x_1^k + \cdots + x_n^k = 0$       340
Diagonal equations, $\alpha_1 x_1^2 + \cdots + \alpha_n x_n^2 = \alpha$       305
Diagonal equations, $\alpha_1 x_1^k + \cdots + \alpha_n x_n^k = \alpha$       394 303—304 319—320 339—340
Diagonal equations, $\alpha_1 x_1^k + \cdots + \alpha_s x_s^k = 0$       340
Diagonal equations, system of      340—341
Diamond, H.G.      55 241
Dickson polynomial      386 440 443
Dickson's Diophantine system for p=5f+1      94 131 151
Dickson's Diophantine system for p=5f+1, analogue for p=7f+1      143
Dickson, L.E.      5 97 131—132 150—152 336—338 384
Dieudonne, J.      56
Difference set      174 181—182
Difference set, Abelian      174
Difference set, cyclic      174
Difference set, modified power residue      174 497
Difference set, planar      174
Difference set, power res due      174—175 181 497
Difference set, supplementary      181
Dilcher, K.      4 164 284 482
Dimitrakoudis, D.      55
Dirichlet      1 54
Dirichlet character      26 379
Dirichlet's class number formula      54 377
Dirichlet's L-function      54; see also “L-function”
Dirichlet, G.L.      1 51 53—54 99 231 264
Discrete Fourier Transform      47 01—52
Discriminant of period polynomial      155—339
Disquisitiones Arithmeticae      1 97
Doerge, K.      210
Drmota, M.      3 172
Du, D.Z.      99
Duke, W.      386
Dunton, M.      338
Dwork, B.      2 211 268 293
Eichler, M.      52
Eigenspace      51
Eigenvalue      47—48 51
Eigenvector      51
Eisensrein prime      234
Eisenstein      1
Eisenstein integer      234
Eisenstein integer primary      236
Eisenstein integer prime      234
Eisenstein sum $E_r(\chi)$       389—400 438
Eisenstein sum $E_r(\chi)$ (over $F_{p^2}$ )      396—399 438
Eisenstein sum $E_r(\chi)$ , congruence for      394 414—415 419
Eisenstein sum $E_r(\chi)$ , of order 10      435
Eisenstein sum $E_r(\chi)$ , of order 12      433
Eisenstein sum $E_r(\chi)$ , of order 16      430
Eisenstein sum $E_r(\chi)$ , of order 2      393
Eisenstein sum $E_r(\chi)$ , of order 20      428
Eisenstein sum $E_r(\chi)$ , of order 24      435—436
Eisenstein sum $E_r(\chi)$ , of order 3      400—101 435
Eisenstein sum $E_r(\chi)$ , of order 4      402 435
Eisenstein sum $E_r(\chi)$ , of order 5      403—404
Eisenstein sum $E_r(\chi)$ , Of order 6      405—406
Eisenstein sum $E_r(\chi)$ , of order 7      412—413 416
Eisenstein sum $E_r(\chi)$ , of order 8      407—406 416
Eisenstein sum $E_r(\chi)$ , order of      390
Eisenstein sum $E_r(\chi)$ , relationship with Gauss sums      391 393 421
Eisenstein's congruences for binomial coefficients      5 414 417—419
Eisenstein's reciprocity law      5 234 267 468 474 494
Eisenstein's reciprocity law for Gauss sums      493—495
Eisenstein, G.      1—5 53 97 264—266 336 338 438 468 494
Elliptic curves      210—211 266 387 466
Equations      see “Diagonal equations”
Error correcting code      369 371
Estenuann, T.      24 52 386
Estermaun's evaluation of a quadratic Gauss sum      24
Euclidean Domain      240 250
Euler, L.      231
Evans      6
Evans, R.J.      2 4—5 51 53 55—56 63 98—99 151—152 171—173 181—182 195 209 211 229 232—233 267—268 293 338—339 385—388 396 400 438—439 453 465—467 494 497—498

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