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

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

Предметный указатель

Lichtenbaum, S.      387—388
Lidl, R.      5 7 56 97 210 336—337 341 385 440
Lienen, H. von      99 232 267
Lift of character      342 356 385
Lin, C.Y.      56
Lindeloef, E.      51
Liorente, P.      231—232 339
Liverance, E.      266
Loeser, F.      97
Lomont, J.S.      2 54
Loxton, J.H.      162 496
Lucas' Theorem      293
Lucas, E.      293
Mann, H.B.      174 181
Masley, J.M.      65
Mathews, G.B.      171 338
Matthews, C.R.      158 162
Mauclaire's evaluation of a Gauss sum      40
Mauclaire, J.-L.      3 31 40 54
McEliece, R.J.      3 385—386 439
McFarland, R.L.      181
McGettrick, A.D.      158 162
Meissner, W.      482
Merrill, K.D.      53
Mertens, F.      52 265—266
Miki, H.      63 336 387—388
Miller, J.C.P.      99
Mills, W.H.      182 385
Milnor, J.W.      55 495
Mitchell, H.H.      97—98 384—385
Moebius inversion      02
Montgomery, H.L.      65 171—172 340
Monzingo, M.G.      195 209—210
Moore, R.A.      53
Morain, F.      183 210 387 466
Mordell      1
Mordell, L.J.      1 51—53 211 255 336
Moreno, C.J.      160 384—385 494
Morita, Y.      277
Morlaye, B.      209
Morley's theorem      293
Morley, F.      293
Mortens      52
Mortimer, B.C.      232
Morton, P.      51
Moser, L.      210
Mullen, G.L.      172 440
Multinomial coefficient      290 336 387
Muskat, J.B.      99 112 150—152 181 231—233 385 438 466—467
Myerson, G.      340 427 439
Nagell, T.      50 231 470
Nakahara, T.      266
Narkiewicz, W.      53—54 56 64—65 98 277 343
Nashier, B.S.      233 272
Nemehenok, J.      53
Nenmann, J. von      159
Neomaan, O.      56 388
Niederreiter, H.      5 7 56 97 210 336—337 341 385 387 438 440
Norm of a prime ideal      468
Norm of an element      60—01 234 356
Normal basis      319 388
Normalized element      63 141 146 150
Normresidue symbol      494
O'Meata, O.T.      494
Odoni, R.      3 31 33 54
Ono, K.      211 467
Ono, T.      336
Oskolkov, K.      55
Ozeki, M.      340
p-adic gamma function      4 2
Padma, R.      183 210
PaJey, R.E.A.C.      181
Pall, S.      232
Parnami, J.C.      99 210 232 292 387 497
Partition of P      see “Quadratic partition of p”
Patterson      1
Patterson's conjecture      100
Patterson, S.J.      1 160 164 171
Pauario, D.      339
Pepin, T.      99 231—232
Peralta, R.      198 210
Perel'muter, G.I.      55
Period of a continued fraction      104
Period polynomial      320 327 338 339 426 139
Period polynomial of degree 2      330 336 427
Period polynomial of degree 3      171 330 338 427
Period polynomial of degree 4      271 330—331 338 435
Period polynomial of degree 5      172 338
Period polynomial of degree 6      171 338
Period polynomial of degree 8      172 338
Period polynomial relationship with cyclotomic numbers      329
Period polynomial, reduced      327 426
Period, f-normal      5 175 182 326 327 338—339 420
Period, f-normal, reduced f-normal      327
Period, f-normal, relationship with cyclotouur numbers      328—329 437 438
Period, f-normal, translates of      338 439
Perott, J.      232
Perron, O.      210
Poincare series      340
Poisson summation formula      43 51
Pollard, H.      241
Pomerance, C.      4 97 164 284 482
Poulakis, D.      210
Power residue symbol      66 235 241 344 474
Power residues      174 181—182;
Power residues, cubic      338
Power residues, octic      179
Power residues, quadratic      see “Quadratic residues”
Power residues, quartic      177—178 292
Power residues, sextic      178
Power residues, twelfth power      179
Primary integer      236 242 265—266 470 473
Prime ideal factorizations of p and q      65 342—343
Primitive root      68 98 470
Projective plane      211
Pulham, J.      5 453
Pure Gauss and Jacobi sums      342 362—363 385—386
Quadratic nonresidues      92—93 196 199 209—210
Quadratic partition of p      101 103—105 107 109 111 114 118 120 125 130 133 136 138 140 143 147—149 197 430 435—436
Quadratic residues      92—93 177 196 209—210
Rabin, M.O.      164 197
Raderuacher, H.      50
Radoux, C.      466
Rajwade, A.R.      79 98—99 152 209—211 232—233 272 291—292 338 387 497
Ramanujan sum      29
Rankin, R.A.      209 211
Rational reciprocity law      251 266
Rational reciprocity law, $2^t \mathrm{th}$       267
Rational reciprocity law, bioctic      258 267
Rational reciprocity law, biquadratic      252 254 266
Rational reciprocity law, cubic      267
Rational reciprocity law, octic      256 267
Rational reciprocity law, quartic      see “Biquadratic”
Reciprocity law for Jacobi sums      495
Reciprocity law, biquadratic      244 262 265—266 336
Reciprocity law, biquadratic, supplement to      247 266
Reciprocity law, cubic      257 264—266
Reciprocity law, cubic, supplement to      240 264 265
Reciprocity law, octic      490 493
Reciprocity law, quadratic      2 15—16 50 52—53 265 306 395
Reciprocity law, quadratic, supplement to      17 43 306—307 337 382
Reciprocity law, quartic      see “Biquadratic”
Reciprocity law, quintic      266
Reciprocity law, quintic, supplement to      266
Reciprocity retetion      474
Representation of p      see “Quadratic partition of p”
Residuacity      212 232—233 338—339; reciprocity”
Residuacity, 11th-power      232
Residuacity, 19th-power      232
Residuacity, 9th-power      232

Residuacity, bioctic      99 228—229 232
Residuacity, biquadratic      see “quartic”
Residuacity, cubic      82 86 99 212—215 230—231 235 239 262 339
Residuacity, octic      99 218—221 227—228 230 232—233 258 263 267 493
Residuacity, quartic      83 91 99 216—217 225—228 230—231 233 249 253 339
Residuacity, quintic      221—223 232—233 339
Residuacity, septic      232
Residue symbol      see “Power residue symbol”
Residues      see “power residues”
Restriction (of a character)      355
Reti, Z.      55
Reuschle      99 263
Reuschle's criterion      99
Reuschle, C.G.      99 232
Richman, D.      340
Riduicae, M.      51
Rishi, D.B.      210
Robinson, R.M.      200
Robinson, S.F.      151 438 466—467
Rogers — Szegoe polynomials      50 54
Root nurabtT      2668
Rosen, M.I.      5—7 9 62 97 234 240—241 251 265 336 385 494—495
Rousseau, G.      53
Rowe, D.E.      53
Roy, R.      35
Rubin, K.      388
Rumely, P.      97
Rumsey, H.      385
Ryset, H.J.      174
Saito, H.      55
Salem number      64
Salie sum      384 336
Salie, H.      210 6
Sands, J.      387
Sarnak, P.      36 386
Sato, H.      293 387
Schaar's identity      52
Schaar, L.      58
Schariau, W.      55 494—495
Schleich, W.P.      3 54
Schmidt, C.-G.      387
Schmidt, H.L.      385
Schmidt, W.M.      183 385
Schoenfeld, L.      51
Schoof, R.      164 338
Schroeder, M.R.      55
Schrutka, L. von      195 209 291
schur      51
Schur, I.      51
Schwermer, J.      495
Scott, C.A.      338
Semiprimary      477 485
Sepanski, M.R.      3 98
Serre, J.-P.      386
Shafarevich, L.      53—54
Shallit, J.O.      164 197 339
Shanks, D.      52 160
Sheehan, J.      5 3
Shimaura, A.      350
Shimura's reciprocity law      495
Shimura, G.      495
Shinoda, K.      385—386
Shioda, T.      336
Shiratani, K.      265—266 293 350 386—387
Shparlinski, I.E.      172 339
Siegel      1
Siegel, C.L.      1 52 55
Singh, S.      209
Skalba, M.      3 172
Skinner, C.M.      340
Skolem, T.A.      265—266 494
Slyer, R.      53 55
Small, C.      7 336 385
Smith, H.J.S.      50 53 97 231 264—265 266 292 339 414 438 494
Smith, L.      152
Smith, R.A.      173 386—387
Snapper, E.      98
Soto — Andrade character sum      4 400
Spackman, K.W.      341
Spearman, B.K.      98 151—152 231 265 293 384 438 494 497
Sperber, S.      387
Spiridonov, V.      3 54
Stanton, D.      5 385 387 453
Stark, H.M.      53 183 210 377 495
Stepanov, S.A.      183 385 387
Stern, M.      211 291
Sterneck, R. von      210
Stickelberger, L.      1 4 98 384—385 438—439
Sticketberger      1 4
Sticketberger ideal      387
Sticketberger's congruence for Gauss sums      344 349 381 384
Storer, T.      98 174 181 209 211
Subbarao, M.V.      231
Sullivan, F.      55 497
Sun, Q.      337
Sun, Z.-H.      267
Sun, Z.-W.      337
Sylvester, J.J.      338
Tabakova, E.D.      160
Takagi, Teiji      494
Takagi, Tsuyoshi      158
Talbot image      54
Tale, J.      495
Tanner, H.W.L.      131 172 232 338
Terwilliger algebra      151
Thaine, F.      98—99 152
Theta function      44 51—52 56 160 265
Thue — Morse fractal function      172
Tietaevaeinen, A.      341
Tihanyi, M.      231
Tolimieri, R.      51—52
Trace      7 51 358 388 438
Tuakur, D.S.      55
Turnwald, G.      440
Uehara, T.      388
Uniform distribution      160 164 171 173 498
Unique factorization      65 234 241 300
Vaaler, J.D.      55
Vaidyanathaswamy, R.      231
van der Corput, J.G.      52
Van der Vlugt, M.      386
Vandermonde determinant      48
Vandiver conjecture      98
Vandiver, H.S.      97—98 336—337
Vaughan, R.C.      160 171—172 340
Venkataraman, S.      183 210
Vinogradov, A.I.      160
Vostokov, S.V.      494
Wahlin, G.E.      97
Walling, L.H.      53
Walum, H.      210
Wamelen, P.B. van      387
Wan, D.Q.      337—339 386
Wang, J.      97 338 340
Ward, R.L.      182 385
Waring's formula      464
Washington, L.C.      63 65 97—98 338 387
Washio, T.      350
Watabe, M.      265—266
Waterhouse, W.C.      51
Watling, N.      3 51—52 54
Webb, W.      293
Weber, H.      51 54 171
Weierstrass $\wp$ -function      157 162 265
Weight (of a code word)      369—370 383
Weil      1 6 171 468
Weil represent at ion      400
Weil — Serre bound      386
Weil's estimate for character sums      183 189 198
Weil's reciprocity law      493

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