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Jones G.A., Singerman D. — Complex Functions: An Algebraic and Geometric Viewpoint
Jones G.A., Singerman D. — Complex Functions: An Algebraic and Geometric Viewpoint

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Название: Complex Functions: An Algebraic and Geometric Viewpoint

Авторы: Jones G.A., Singerman D.

Аннотация:

Elliptic functions and Riemann surfaces played an important role in nineteenth-century mathematics. At the present time there is a great revival of interest in these topics not only for their own sake but also because of their applications to so many areas of mathematical research from group theory and number theory to topology and differential equations. In this book the authors give elementary accounts of many aspects of classical complex function theory including Möbius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. A distinctive feature of their presentation is the way in which they have incorporated into the text many interesting topics from other branches of mathematics. This book is based on lectures given to advanced undergraduates and is well-suited as a textbook for a second course in complex function theory. Professionals will also find it valuable as a straightforward introduction to a subject which is finding widespread application throughout mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 356

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{\infty}$ alias      191
$\Gamma$-automorphic      266
3-manifold      331
Abel, N.H      72
Abikofr, W.      274
Absolute convergence (of an infinite product)      84
Abstract Riemann surface      169
Addition theorem      115
Addition theorem for $\wp$      118
Ahlfors, L.      333
Algebraic function      184
Algebraic group      119
Amplitude (of a cusp)      306
Analytic at $\infty$      5
Analytic atlas      168
Analytic continuation      125
Analytic continuation along a path      138
Analytic function      1
Analytic function element      123
Analytic function on a Riemann surface,      172
Analytic germ      177
Angle (between curves)      37
Angle (between H-lines)      229
Anti-automorphism (of $\Sigma$)      19
Antipodal map      40
Antipodal point      40
Atlas      168
Aulomorphism (of the Riemann sphere)      17
Automorphic function      231 266
Automorphism (of a lattice)      120
Automorphism (of a Riemann surface)      200
Basis (for a lattice)      59 65
Beardon, A.F.      225 331
Bers, L.      74
Bolyai, J.      221
Branch      140
Branch-point      13 107 207
Branch-point of order k-1      18 183 207
Branched covering      13 207
Branched Riemann surface (of a germ or equation)      184
Cauchy integral formula      318
Cauchy — Riemann equations      318
Cauchy's theorem      318
Centraliser      220
Characteristic subgroup      269
Chart      168
Circle (in $S^2$ or $\Sigma$)      21
Classical Schottky group      332
Closed path      138
Co-prime (polynomials)      8
Commutator subgroup      270
Compact      3
Compatible (atlases)      168 191 192
Complete global continuation      184
Complex plane, I complex projective line      20
Complex structure      169
Concyclic      28
Conformal equivalence      198
Conformal homeomorphism      198
Conformal map      36
Conformally equivalent      198
Congruence (modulo $\mathbb{Z}$)      62
Congruence (modulo a lattice)      66
Congruence subgroup      301
Congruent sides      247
Congruent vertices      245
Conjugacy class      32
Conjugate elements (of a group)      32
Conjugate point      28
Convergence (of an infinite product)      83 85
Conway, J.H.      283
Coordinate transition function      168
Covering map      13 206
Covering space      13
Covering surface      206
Critical point      185
Cross-ratio      24 27
Crystallographic restriction      120
Cusp      306
Cycle (of vertices)      245
Cyclic quadrilateral      28
D-neighbourhood      177
Defining relations      325
Degree (of a rational function)      8
Degree (of an algebraic function)      184
Differential equation for $\wp (z)$      97
Dihedral group      45 46
Direct analytic continuation      124
Direct meromorphic continuation      124
Directly conformal      37 323
Dirichlet polygon      68
Dirichlet region (for a Fuchsian group),      241
Dirichlet region (for a lattice)      68
Dirichlet tessellation      241
Dirichlet, G.P.L.      68
Disc (in $\Sigma$)      30
Disc centred at a      177
Discontinuous group action      208
Discrete subgroup      61
Discrete subset      57
Discriminant      274 329
Doubly periodic      59
Duplication theorem      118
Edge (of a polygonal subdivision)      193
Eisenstein series      96
Elementary neighbourhood      206
Elliptic curve      109
Elliptic cycle      245
Elliptic cyclic group      232
Elliptic function      72
Elliptic integral      72
Elliptic transformation      35 219
Elliptic vertex      245
Entire function      292
Euclidean length      222
Euler — Poincare formula      196
Euler, L.      116
Eulet characteristic      194
Extended complex plane      1 2
Face (of a polygonal sundivision)      193
Fagnano, C.G.      116
Fibre      206
Field      6 98
Fischer — Griess monster group      283
fixed-point      32
Fourier, J.B.J.      64
Free product      299
Fuchs, L.      231
Fuchsian group      231
Function element      123
Fundamental group      148
Fundamental parallelogram      66
Fundamental polygon      66
Fundamental region (for a Fuchsian group),      240
Fundamental region (for a lattice)      66
Galois group      52 190
Gamma-function      127
Gauss, C.F.      72 271
Gauss-Bonnet formula      229
Gaussian integers      235
General linear group      18 19
Genus (of a Fuchsian group)      307
Genus (of a surface)      163 193
Germ      177
Great circle      50
Green berg, L.      333
H-circle      227
H-invariant      225
H-line      224
H-line segment      223
H-reflection      237
Hadamard's gap theorem      134
Hamilton, W.R.      42
Heine — Borel theorem      3
Holomorphic function      1 173
Homotopic      141
Homotopy      141
Homotopy class      141
Hurwitz formula      196
Hurwitz group      264 300
Hurwitz, A.      264
Hyperbolic 3-space      331
Hyperbolic area      228
Hyperbolic circle      227
Hyperbolic cyclic group      232
Hyperbolic distance      224
Hyperbolic geometry      221
Hyperbolic length      222
Hyperbolic line      224
Hyperbolic line segment      223
Hyperbolic metric      224
Hyperbolic plane      224
Hyperbolic polygon      228
Hyperbolic surface-area      332
Hyperbolic transformation      35 219
Hyperbolic volume      332
Hyperbolically convex      230
Hyperbolically starlike      230
Indirectly conformat      37 323
Infinite product      83 85
Inverse (of a path)      147
Inversion (in a circle)      28
Isolated vertex      269
Isometric circle      54
Isometry      37
Jacobi, C.G.J.      72
Jacobian      191
k-transitive      23
Kiemann zela-function      91 280
Klein, F.      167
Kleinian group      332
Lattice      59 65
Legendre's relation      102
Lehner, J.      247
Length (of an orbit)      44
Level      301 308
Lift      203
Limit set      235 332
Linear fractional transformation      17
Liouville's theorem      319
Lobatchewsky, N.I.      221
Local coordinate      168
Local uniformising parameter      183
Locally finite fundamental region      244
Logarithmic derivative      88
Loxodromic transformation      35 220
Lune      50
Lyndon, R.C.      42
Macbeath, A.M.      269
Maskit, B.      259
Maximum-modulus principle      323
Meromorphic at $\infty$      5
Meromorphic continuation      125
Meromorphic continuation along a path,      138
Meromorphic continuation of a germ      179
Meromorphic function (on $\Sigma$)      6
Meromorphic function (on a Riemann surface)      174
Modular function      276
Modular group      232 272
Moduli space      273
Modulus (of a lattice)      272
Moebius band      191
Moebius transformation      17
Moebius, A.F.      17
Monodromy group      166
Monodromy theoiem      146
Monster simple group      283
Morera's theorem      319
Multiple point      7
Multiplicity      6
Multiplier      34
n-manifold      168
Natural boundary      133
Non-Euclidean geometry      221
Norm      81
Normal convergence (of an infinite product)      86
Normal convergence (of an infinite series),      81
Normaliser      240
Norton, S.      283
Null-homotopic      143
Number of sheets      206
Omits a value      292
One-point compactification      4
Open mapping      12 320
Orbit      44
Orbit-space      71
Order (of a branch-point)      13 207
Order (of a meromorphic function at a point)      10 215
Order (of a rational function)      8
Order (of a transformation)      35
Order (of an elliptic function)      73
Ordinary set (of a Kleinian group)      332
Orientable      192
Orientation      193
Orientation-preserving      192
Parabolic class number      303
Parabolic cyclic group      232
Parabolic subgroup      303
Parabolic transformation      35 219
Parabolic vertex      255
Partial fractions      16
Path      137
Period (of a Fuchsian group)      246
Period (of a function)      56
Period (of a transformation)      35
Periodic function      56
Picard's theorem      292
Picard, C.E.      289
Poincare, H.      221 259 331
Point at $\infty$      2
Polygonal subdivision      193
Presentation      238 325
Principal congruence subgroup      301
Principal pert      7
Principal value of log Z      83
Principle of permanence of identical relations      180
Product (of paths)      147
Projective general linear group      18 20
Projective special linear group      19 20
Projective special unitary group      41
Properly discontinuous group action      232
Puiseux series      183
Puiseux, V.      183
Pythagoras' theorem      68
Quaternion algebra      42
Quaternion group      42
Quotient-space      71 248
Rado, T.      194
Ramanujan's tau-function      283
Ramified covering map      207
Rational elliptic curve      119
Rational function      8
Real elliptic curve      111
Real lattice      111
Real meromorphic function      111
Real projective plane      71
Real rectangular lattice      113
Real rhombic lattice      113
Reduced word      297
Region      1 5
1 2
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