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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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Предметный указатель
Abel 239 269 275 Addition formula 241 279 Adkisson 201 Adleman 26 139 Adler 140 275 276 347 Agarguen 20 Agou 417 Agrawal 142 343 Ahlborn 23 Aigner, A. 23 70 171 173 174 227 228 310 313 Aigner, M. 12 Ailing 277 Al — Hogendi 395 Aladov 26 Alderson 141 Alexejewsky 415 Algebraic integer 43 Allander 417 Ambiguous, ideal 47 Ambiguous, ideal class 47 Anderson 382 Andrews 103 Ankeny 141 416 Anshel 228 Anti-units 384 Antropov 11 Apery 343 Armitage 390 Arndt 69 Artin ix xiii 25 136 201 204 341 344 349 Artin root number 390 Artin symbol 86 87 114 130 383 Arwin 170 415 Aubry 11 23 25—27 170 415 Auslander 139 417 Ayoub 267 BACH 25 119 Bachet 1 11 Bachmann xii xiv 11 18 100— 102 179 200 227 277 342 395 Backlund 20 Bambah 103 Banderier 24 Bang 414 Barbilian 416 Barcanescu 417 Barkan 278 343 Barner 11 Barnes 417 Barrucand 118 137 173 417 Bartelds 415 Bass 21 70 Bauer 384 Baumgart xiv 14 24 101 Bayad 277 Beach 175 Beeger 141 310 312 Beilinson conjecture 344 Bennett 26 Bernardi 141 175 Berndt, B. 23 138—140 146 201 293 310 393 417 Bernoulli numbers 276 329 343 375 394 Bernoulli numbers, generalized 332 Bernoulli polynomials 333 Bernoulli, Jak 267 343 Bernoulli, Joh 267 Berrizbeitia 228 231 Berry 228 231 Bertolini 396 bessel 15 beta function 139 Beuker 202 Bhaskaracharya 11 Bianchi 170 Bickmore 70 179 205 229 310 Biermann 34 272 Bierstedt 27 Biihler 11 billing 175 Bindschedler 277 Binet’s formula 73 Birch xii 21 385 417 Birch — Tate conjecture 385 387 Birkhoff 27 Blanchard, A. 70 Blanchard, C. 70 Bloch — Kato conjecture 344 Bock 70 414 Boelling 175 Boge xv Bohnicek 201 277 312 393 Bombieri 345 Bonaventura 170 277 Borchardt 271 Borel 344 Borevich xii 60 70 Bork 29 Borwein, J.M. 269 Borwein, P.B. 269 Bouniakowski 23 25 413 Brahmagupta 11 Brandis xv Brandler 172 173 176 Brandt 170 226 416 Brauer, A. 20 26 27 310 Braun, H. 141 Braun, I. 13 Bray 73 Brenner 23 417 Bressoud 103 Brewer 313 416 Bricard 25 270 Brillhart 12 27 70 185 Brinkhuis 390 391 Brown 4 20 21 33 70 172 173 175 176 417 Brumer 383 385 Brylinski 417 Bucher 312 Buehler 394 Buell 174 175 312 313 Bugaieff 26 277 Burde 26 166 171 201 227 310 416 Burkhardt 11 Burnside 141 313 Busche 23 170 201 414 415 Bussey 13 Cabillon 269 Cailler 228 Canuto 396 Carcavi 12 Carey 228 Caris 26 Carlitz 23 27 103 137 141 416 Carrega 101 Cartier 23 345 Cassels 60 175 229 Cassou — Nogues 311 Castaldo 417 Cauchy 15 31 102 138 202 269 270 313 357 390 394 413 Cayley 100 141 201 228 Cerone 415 Chahal 344 Chang 20 26 Chapman xv 389 395 Character, additive 127 Character, Dirichlet 121 Character, multiplicative 127 Character, primitive 71 105 122 Character, real 124 Chebotarev x 103 170 chebyshev 22 Chevalley x Chinburg 390 Chowla, P. 25 Chowla, S. 25 103 138 140 201 202 225 228 342 396 416 Christol 345 Chua 23 Chum an 174 Cipolla 26 Clarke 18 Class group, genus 47 Class group, narrow 46 47 Class group, wide 46 Class number formula 100 105 277 307 308 312 Clausen 227 Coates xii 387 391 394 395 Cochrane 16 Cohen, E. 140 Cohen, H. 12 26 139 142 Cohen, S.D. 141 Cohn 69 74 173 277 399 Collins 26 Collison 25 201 225 Complex multiplication 187 245 249 263 Conductor 122 Conductor, -discriminant formula 125 335 Congruence, Eisenstein’s 255 Congruence, Euler’s 238 255 Congruence, Gauss’s 192 202 203 conjugate 43 Conrad 391 397 Conrey 343 Constructible 104 Convolution 134 Cooke xv 224 228 Cooper xiii 23 26 Cornacchia 12 342 Cornaros 25 Cornell 396 Corrales — Rodriganez 137 Cosgrave 231 Cowles, J. 228 Cowles, M. 228 Cox 11 23 263 396 Craig 229 Crandall 394 401 Crelle 269 Cremona 17 Crstici 27 Cuculiere xv 1 8 24 Cunningham 171 201 226 310 Currie 202 Cusp form 263 Cyclotomic numbers 101 106 145 223 230 321 322 Cyclotomic polynomial 81 83 101 Cyclotomic units 97 386 Dalen 137 Dantscher 225 277 Darmon 396 Davenport 16 23 132 138 340 344 391 397 Davenport — Hasse relation 128 132 138 Davenport — Hasse theorem 133 328 350 398 De La Vallee Poussin 69 330 415 De Seguier 103 Decomposition field 75 Decomposition group 75 79 125 Dedekind 22 25 26 69 81 84 95 101 125 225 228 229 274 276 342 344 413— 415 Defining modulus 122 Degree 248 delaunay 103 Delcour 395 Delezoide 23 Deligne xii 345 383 Deloup 141 Delsarte 23 Deninger 346 Dennis xv Deuring 342 diamond 396 Dickson xiii 12 14 21 141 145 175 225 342 343 Dieter 23 Dieudonne 345 Difference set 201 Digby 3 12 Dilcher 401 DIMENSION 341 Dintzl 201 225 276 277 Diophantus 1 11 14 Direct limit 66 Directed set 400 Dirichlet xiii 4 7 19—21 26 27 70 102 137 153 167 170 171 174 175 199 209 256 270 343 375 413 Dirks 24 Discriminant 43 116 Discriminant, prime 45 Dittmar 225 Divisor 247 Divisor, principal 248 Dockeray 416 Doerge 26 416 Doerrie 170 226 Dressier 24 Dudeney 395 Dummit 384 Dunton 225 228 Duplication formula 241 268 Dupre 20 Dwork 202 345 Dym 139 E-primary 217 Edwards 13 16 274 343 396 Eichenberg 23 Eichler 417 Eisenstein vii 10 16 24 26 31 114 136 137 139 201 203 209 225 236 270 281 310 313 340 366 390 392 413 Eisenstein series 249 263 Eisenstein sum 133 139 373 El Hassani 278 Elliptic curve 396 Elliptic function 247 Elliptic integral 267 Ely 30 417 Em vail 379 394 395 Embedding 43 Enneper 269 277 Ennola 173 Epstein 136 175 176 Erchinger 100 Erez 390 Errera 20 Esrafilian 25 Estermann 103 Estes 26 172 Euler vi 3 11 13 70 100 131 175 201 222 229 268 276 329 343 394 Euler numbers 378 387 394 Euler product 329 Euler system 387 Euler’s criterion 4 Evans 138—141 146 173 174 201 202 215 293 299 310 313 343 393 417 Exponential sum 97 346 Eymard 36 Faddeev viii Fagnano 267 Faulhaber 343 Federer 387 Federighi 70 Fee 395 Feigner xv 201 226 230 Feng 25 Fenster xiii Fermat numbers 4 70 72 73 203 231 314 Fermat prime 59 104 Fermat, P. 1 11
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