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Lemmermeyer F. — Reciprocity Laws: From Euler to Eisenstein
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Название: Reciprocity Laws: From Euler to EisensteinАвтор: Lemmermeyer F. Аннотация: This book is about the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisenstein's reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 516Добавлена в каталог: 05.04.2008Операции: Положить на полку |
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Lehmer, D.N. 26 Lehmer, E., v 27 70 85 101 102 137 140 141 162 166 167 171 173 174 203 212 228 343 Leibniz 12 Lemmermeyer 30 166 173 176 181 417 Lemniscate 239 Lemniscatic sine 239 300 Lenstra, A.K. 139 Lenstra, H.W. 26 59 70 73 89 102 137 139 395 Leonard 140—142 174 175 310 Leopoldt 70 137 343 377 385 386 Leopoldt’s conjecture 385 Leprevost 141 Lerch 21 24 102 414 415 Lewandowski 225 277 Lewy 416 Li 138 139 345 346 Libri 25 269 342 Lichtenbaum 138 Lidl 139 140 345 Lietzmann 201 Lind 175 Linden 26 Liouville 15 269 275 413 Lippert 378 Lipschitz 23 271 Littlewood 344 Liverance 228 Llorente 142 Local-global principle 389 Loewy 25 100 Longo 136 Loos 26 Lorenzini 345 Louboutin xv 170 Loxton 278 Lubelski 103 137 Lubin 103 Lucas 56 72 395 414 Lucas numbers 73 Lucas — Lehmer test 70 91 92 Ludwig 22 Lueneburg 275 Mackenzie 394 Mahnke 12 Mahoney 11 Main Conjecture 379 385 Manders 26 Mandl 23 Manin 22 344 Mansion 414 Mantel 25 Markuschewitsch 269 Martinet xv 229 389 Masahito 277 Maser 18 Massell 174 Mathews 270 277 Mathieu 26 101 413 Matrot 25 Matter 276 Matthews, C. 267 Matthews, K. xv Mattuck 345 Mayer 136 Mazur 343 379 386 McClintock 26 McEliece 138 McGettrick 278 McGuinness 175 McKean 139 Mel’nikov 24 270 277 Merindol 417 Meromorphic 243 Merrill 25 mersenne 56 Mersenne numbers 4 70 73 315 Mersenne prime 168 206 Mertens 18 69 103 201 226 277 391 415 Metsankyla 375 394 395 Meyer, C. 278 416 Meyer, P. 270 Meyer, S. 26 Mihailescu 92 139 Miller 26 Mills 27 Milnor 21 70 385 417 Minding 28 Minkowski 16 20 Minkowski bound 55 Minnigerode 170 Minus class group 373 Mirimanoff 137 402 415 Mitchell, H. 394 Mitchell, P. 16 Mitrinovic 27 Mitzscherling 100 Miyagawa 275 Modular function 263 Mollin xv 25 69 215 Monagan 395 Monsky 345 Monzingo 26 140 342 Morain 92 141 146 Mordell 16 28 103 174 175 Moreau 20 Moree 70 Morehead 70 Moreno 278 349 391 396 Morlaye 342 Mortimer 142 Morton 24 175 Motose 417 Movahhedi 137 Murty, K. 396 Murty, R. 396 Muskat 175 228 343 Nagaev 270 Nagell 202 227 Nakamula 278 Nakhash, xv 73 418 Narkiewicz 390 Naryskina 276 Nashier 141 Nasimoff 26 277 Naur 25 Nekovar 385 395 Nemenzo 69 Neukirch 248 Neumann xii 16 22 34 100 103 274 Newman 330 Niederreiter 139 140 345 Nielsen 25 Niemeyer 276 277 280 Noether 389 Nogues 396 Nonsingulax 337 Norm 43 127 349 Norm residue viii Norm residue symbol 60 Normal integral basis 83 387 Olbers 15 96 Oltramare 25 Ono 70 136 139 Onuki 103 Opolka 11 16 18 265 Ore 25 Ostwald 24 Ouyang 382 Padma 141 Pall 26 136 142 172 Panaitopol 275 Park 225 Parnami 141 142 343 Partially ordered 400 Pascal 12 Patterson 18 278 Paucker 100 Pedersen 349 Peitz 226 Peklar 417 Pell 11 Pellet 73 116 137 202 225 227 229 342 414 Pell’s equation 11 44 Pengelley 10 11 21 Pepin 13 15 20 22 23 59 72 102 141 142 174 175 181 224 225 269 342 393 395 414 415 Period equation, cubic 210 223 228 278 Period equation, e-th 102 Period equation, general 84 Period equation, octic 313 Period equation, quadratic 21 95 Period equation, quartic 201 Period equation, quintic 141 Period equation, sextic 228 Period lattice 247 Perott 175 310 313 Perrin — Riou 387 petersen 100 414 Pethoe 13 Petin 138 Petr 103 201 225 226 277 415 416 Pexider 26 Pfleiderer 100 Phong 26 Pickert 23 Pieper xv 5 18 20 24 139 200 Pierpont 100 Piltz 20 Pinch 311 pink 378 Pocklington 25 26 90 175 415 Pollaczek 377 Polya 105 Pomerance 139 401 Popovici 23 Porcelli 136 Postnikov 140 345 Poulakis 141 Prasolov 270 275 277 Primality test 85 88 Primality Test, Lenstra 92 232 Primality test, Lucas — Lehmer 56 Primality test, Pocklington 90 Primary 191 209 221 289 Prime, inert 44 Prime, irregular 375 Prime, ramified 44 Prime, regular 357 375 Prime, split 44 Product formula 53 54 64 Projective, algebraic set 341 Projective, limit 401 Projective, space 341 Projective, system 401 Projective, variety 341 Propp xv Quadratic form 9 21 Quadratic period 95 Quellet 275 Queyrut 390 Quillen 385 387 Rademacher 416 Rajwade 101 140—142 313 342 343 Rameswar 23 Ramification field 75 Ramification group 75 Rankin 141 Rapoport 344 Rashed 11 395 Ray class field 261 Reciprocity law, Artin’s ix 119 Reciprocity law, Burde’s 159 167 188 204 Reciprocity law, cubic 209—232 Reciprocity law, cubicin 2 220 Reciprocity law, Eisenstein’s vii 136 296—299 357 365 392 Reciprocity law, Hilbert’s viii 64 70 201 Reciprocity law, Lehmer’s 167 Reciprocity law, octic 289 304 Reciprocity law, quadratic vi 4 10 23 24 28 30 31 43 47 50—52 60 64 71 80 81 85 88 95 96 100 101 103 200 223 335 Reciprocity law, quadratic in 209 Reciprocity law, quadratic in 154 188 Reciprocity law, quadratic, general viii Reciprocity law, quartic vii 194 Reciprocity law, quartic in 198 Reciprocity law, rational xiii 153 Reciprocity law, rational, cubic 227 Reciprocity law, Rummer’s viii Reciprocity law, Scholz’s 102 160 162 167 Reciprocity law, Scholz’s octic 307 Reciprocity law, sextic 216—219 Redei 22 26 70 172 174 175 181 204 415 Reich 26 Reichardt 23 137 173 175 310 416 Relative class group 373 Replogle 389 Reshetukha 225 278 417 Residue symbol, general 111 Residue symbol, rational 153 Reuschle 141 205 310 392 Reynolds 27 Ribenboim 342 396 402 Ribet 377 378 383 396 Richelot 100 Rideout 385 Rieger 22 Riemann 200 329 343 Riemann hypothesis 132 329 335 341 Riese 103 Riesz 24 416 Ring class field 225 Rishi 141 Robba 345 Roberts 24 Robinson, D. 202 Robinson, R.M. 70 Roblot 384 Rocci 26 Rogers 20 417 ROLL 70 141 Root number 335 Roquette xv 344—346 rose 175 Rosen, K.H. 23 25 Rosen, M. xii 30 79 103 104 136 139 269 270 345 349 391 393 394 Rosenberg 21 Rousseau 24 31 417 Rowe 201 Rubin 357 387 389 395 Rumely 139 Rummer’s Lemma 375 Rumsey 138 Rusin 17 Russinoff 25 417 Ryan 25 Saalschuetz 26 Saidi 228 Salie 395 Salvadori 103 139 Sandor 27 Sands 384 Sangani — Monfared 25
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