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Gray J.J. — Linear Differential Equations and Group Theory from Riemann to Poincare
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Название: Linear Differential Equations and Group Theory from Riemann to PoincareАвтор: Gray J.J. Аннотация: This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and non-Euclidean geometry.
Язык: Рубрика: Математика /Симметрия и группы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: второеГод издания: 2000Количество страниц: 179Добавлена в каталог: 29.04.2005Операции: Положить на полку |
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Abel, H. xvi Abelian functions 21 25 28 30 42 43 50 146 148 168 171 177 217 Accidental singular point 43 59 63 64 284 Algebraic addition theorem 32 Algebraic curve 82 121 141 146 148 152 185 193 194 211 212 265 294 298 Analytic continuation by Gauss 10 Analytic continuation by Poincare 175 Analytic continuation not by Kummer 16 Anosov and Bolibruch xiii 239 243—245 Appell, P. 278 Arithmetico-geometric mean (agm) 3 Beltrami, E. 255 Bernoulli numbers 8 35 Bernoulli, Jakob 31 Betti, E. 121 122 125 Bianchi, L. 184 Biermann, K.R. 56 Birkhoff, G.D. 240—243 Bitangents to a quartic 144 145 146 152 162 Bolyai, J. 193 253 258 Bottazzini, U. 283 294 Boulanger, A. 274 Boundary cut (Querschnitt) 22 Branch point 23 Brioschi, E 86 96 124 125 Briot and Bouquet 29 43 96 Casorati — Weierstrass 30 43 Cauchy, A.L. 28—30 Cayley, A. 47 256—258 Clebsch, R. 148 152 Clemens, H. 50 Connectivity (order of) 22 Dedekind introduces Klein’s J -function 110 Dedekind, R. 107 Dedekind, R., 111 Dedekind, R., on Galois theory 119 Dedekind, R., on modular functions 107 108 114 115 Dirichlet principle 23 55 148 191 223 224 228—230 Elliptic functions 3 14 20 30 55 73 101 104 110 114 124 126—128 135 177—179 181 184 186 195 204 205 216 219 227 236 273 274 281—283 296 298 Elliptic functions, invariants of 127 Elliptic integrals xvi 4 11 12 20 31 54 101 127 147 157 168 184 215 216 292 Equations of Fuchsian class 46 Erlanger Programm 76 83 Euler, L. 1 2 31 32 275 Factorial function of Gauss 7 Factorial function of Legendre 7 Forms, theory of (invariant theory) 76 82 Forsyth, A.R. 85 217 219 Freudenthal, H. 28 120 198 199 283 Fricke, R. 220 221 225 265 301 Frobenius, G. 55 Frobenius, G., on Fuchs’ work 55 Frobenius, G., on irreducible equations 57 Frobenius, G., on Thome’s work 61 Fuchs, L.I. 42 101 115 178 180 Fuchs, L.I., on hge 49 Fuchs, L.I., on Picard — Fuchs equation 50 Fundamenta Nova 12 127 216 Galois group 84 161 Galois, E. 115 Gauss, C.F. 2—11 33 235 Geiser, C.F. 146 Gilain, Ch. 28 29 Goethe, J.W. 300 Gordan, P. xv 69 76 Gordan, P., all solutions algebraic problem 88 Goursat, E. xiii 278—280 Grenzkreis theorem 199 Group theory 76 Halphen, G.H. 95—97 157 169 Hamburger, M. 61 62 210 232 248 295 Hawkins, T. 62 248 260 285 292 300 302 Heaviside, O. 275 277 278 Hermite, Ch. xvi xvii 25 27 54 65 77 80 95 97 101 104—108 111 114 118 122—126 134 135 166 168 169 176 178 183 184 236 259 279 292—294 300 Hermite, Ch., solution of quintic, xvi 101 122—124 Hesse, O. xvii 98 99 142 144 146 152 162—164 166 296 Hesse’s group 291 hessian 80 84 86 89 96 126 142 156 289 292 295 296 Heun’s equation 67 Hilbert, D. 148 220 224 234 237—239 241 245 263—265 Hurwitz, A. xviii 64 112 157 184 188 196 199 270 297—299 Hypergeometric equation (hge) xiii xv xvi 1 2 5 10 15 16 18 20 23—28 34 48—50 54 58 69 73 75 81 85 86 111 128 170 183 184 187 219 220 224 231 232 234 236 271 275 276 278 287 Hypergeometric series (hgs) 1 3 11 14 15 23 27 34 58 59 70 73 111 181 183 229 276 278 279 281 283 286 287 Hypergeometric series (hgs), compared to P-functions 26 111 icosahedron 73 81 83 84 86 126 133 134 290 297 Indicial equation 41 47 49 52 53 57 59—61 64 170 171 178 184 211—215 218—220 270 285 Invariant theory 69 75 76 79 82 83 87 88 95 120 126 200 J-function 127—131 161 Jacobi, C.G.J. xvi 1 3 11—14 20 28 104—106 114 116 123 124 126 142—144 146 148 149 152 168 176 215 216 237 283 286 296 Jacobi, C.G.J., on inversion 170 Jordan, C. 76 89—95 146 Jordan, C., his canonical form 61 62 Klein, C.F. xv—xx 2 3 6 16 25 65 69 73 76 77 80 82 152 185 203 258 260 264 298 Kleinian functions named 193 Koebe, P. xiv 263—266 Koenigsberger, L. 42 52 106 Kronecker, L. 14 42 74 77 88 101 115 118 119 124—126 166 228 293 296 298 Kronecker, L., on Galois theory 115 117 121 Kummer, E.E. xvi 11 14—18 20 23 28 42 46 124 258 279 283 Lame’s equation 65 168 Laurent, PA. 30 43 284 Legendre, A.M. xvi 3 7 11 20 33 54 216 254 Legendre’s equation xvi xvii 5 11 13 14 37 38 54 102 114 184 212 Legendre’s relation 34 54 285 286 Liouville, J. 49 50 116 168 273 274 301 Lobachevskii, N.I. 182 193 253—258 Lutzen, J. 49 273 Mathieu’s equation 65 Mobius transformations 36 73 217 264 301 Modular equations xviii 101 113—117 121—127 132—135 137 141 152 157 161 166 219 293 Modular functions xv—xix 1 54 101 104 123—126 132 133 136 152 161 177 184 188 193 198 265 296 298 monodromy xv—xvii 10 16 25—27 37 38 41 47 51—53 55 69 78 80 84 86 90 92 94 96 98 102 105 106 118 134 170 209 210 214 215 217 219 220 233 237 238 243—245 268 272 273 287 292 Monodromy, matrix of 38 43 44 46 54 61 62 102 106 210 232 238 239 243 248 Natural boundary 74 103 229 Neuenschwander, E. 30 42 43 196 283 288 296 Neumann, C.A. xviii 185 Newton, I. 31 141 Non-Euclidean geometry xix 82 95 99 120 180 182—184 186 188 189 192 193 196 200 201 204 209 221 Non-Euclidean geometry, history of 253 P-function of Riemann xix 23 24 26 27 39 72 111 232 234 235 279 287 Papperitz, E. 27 37 Pepin, J.F.T. 273 274 303 Pfaff, J.F. 2 3 6 Picard — Fuchs equation 50 Picard, E. xiii 168 169 188 267—271 278—280 301 Plemelj, J. xiii 219 220 239—243 Plucker, J. xvii 120 141—145 152 Plucker’s paradox 143 Pochhammer’s differential equation 279 Poincare, H. 173 Poincare, H., writes to Fuchs 173 Poncelet, J.V. 142 143 274 Prym, F 46 185 Puiseux, V. 27—29 48 284 Purkert, W. 108 119 120 288 Richards, J. 256 Salmon, G. 151 295 Schlafli, L. 23 27 105—107 138 139 Schlesinger, L. xiii 42 103 113 219 220 231 239 267 268 272 281 282 Schlissel, A. 55 Scholz, E. 254 255 284 296 301 Schottky, R 190 194 195 199 217 223—225 265 Schwarz reflection principle 225 Schwarz, H.A. xv 70—75 189—191 Schwarzian derivative 71 Singer, M. xiii 273 274 Singular moduli 104 Singular point 44 Steiner, J. 145 146 152 295 Stillwell, J. 213 255 Syddall, R. 98 99 Sylow theory 90 92 93 118 Tannery, J. 61 62 105 Theta function 148 177 181 184 187 296 Theta-Fuchsian 181—184 187 193 196 208 209 214 216 Thomae, J. 55 286 287 Thome, L. 42 55 59—61 214 287 Toth, I. 256 302 Transvectant (Uberschiebung) 84 Uniformization theorem 193 203 val (Dedekind’s function = Klein’s J-function) 110—113 Wallis, J. 2 Weierstrass, K. xix 1 3 14 21 23 30 42—45 50 56 62 74 127 146—148 Wussing, H. 76 117 118 282 288 Zeta function 23 177 215 216 Zeta-Fuchsian function 183 193 198 201 209 215—217 219 239
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