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Lewin L. — Structural properties of polylogarithms
Lewin L. — Structural properties of polylogarithms

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Название: Structural properties of polylogarithms

Автор: Lewin L.

Аннотация:

Years ago, the handful of peculiar numerical dilogarithmic identities, known since the time of Euler and Landen, gave rise to new discoveries concerning cyclotomic equations and related polylogarithmic ladders. These discoveries were made mostly by the methods of classical analysis, with help from machine computation. About the same time, starting with Bloch's studies on the application of the dilogarithm in algebraic $K$-theory and algebraic geometry, many important discoveries were made in diverse areas.
This book seeks to provide a synthesis of these two streams of thought. In addition to an account of ladders and their association with functional equations, the chapters include applications to volume calculations in Lobatchevsky geometry, relations to partition theory, connections with Clausen's function, new functional equations, and applications to $K$-theory and other branches of abstract algebra. This rapidly-expanding field is brought up to date with two appendices, and the book concludes with an extensive bibliography of recent publications. About two-thirds of the material is accessible to mathematicians and scientists in many areas, while the remainder requires more specialized background in abstract algebra.


Язык: en

Рубрика: Математика/Анализ/Специальные функции/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 214

Добавлена в каталог: 15.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C[[X]]^{*}$      212
$e^w$      213
$E_n$      218
$f^{-1}(a)$      206
$L(\pi_1(X,x))$      212
$Lie(\pi_1(Y,y))$      217
$Li_n(z;x)$      219
$Li_n(z;x,\gamma)$      218
$l_X(z;x)$      213
$l_X(z;x,\gamma)$      215
$l_X^{\alpha}(z;x)$      215
$l_X^{\alpha}(z;x,\gamma)$      215
$\int_x^z$      205
$\int_{x,y}^z$      205
$\Lambda_x(e_1^{n_1},...,e_k^{n_k})(z)$      213
$\lambda_X(z;x)$      213
$\lambda_X(z;x,\gamma)$      213
$\mathbb{C}[[H_1(X,\mathbb{C})]]$      212
$\mathbb{C}[[X]]$      212
$\mathscr{L}_v(z;x)$      217
$\mathscr{L}_v(z;x,\gamma)$      217
$\mathscr{L}_{e_n}(z;x)$      220
$\omega_X$      212
$\overline{l.d.t.(n)}$      209
$\pi(x)$      212
5-cycle      236
5-cycles equivalent      236
5-term equation      335
a is dependent on A      251
A*(X)      211
Abel      2 4 6 185 193 194
Abel equation      2
Abouzahra      123 370
Absolute Hodge cohomology      347
Accessibility      4 17 18 64 65 71 97
Accessible ladder      40 44
Accessible relations      291
Accessible results      62
Acreman      298
Adamchik      359
Adjoint      114
Adjoint equation      108
Adjoint set      115 119
Alg(G(X))      216
Andrews      19 297 298
Apery      46
Automorphic functions      11 29 185
Automorphism groups      185
Barrucand      24
Base      6
Base $\Gamma$      152
Base $\Omega$      151
Base $\rho$      125 150
Base equation      11 34 84 87 90
Base on the unit circle      8
Bass theorem      158
Beilinson      275 383 391
Birkhoff      155
Bloch      xiii 15 134 136 141 163 290 333 334 382
Bloch dilogarithm function      8
Bloch — Wigner      161
Bloch — Wigner dilogarithm      245 334 345 380
Bloch — Wigner function      123 135 141
Boehm      302
Bombieri      46 141
Borel      330 382
Boyd      160 165
Browkin      xiii 9 23 69 91 92 151 167
Catalan constant      9 243 358 362
Cheeger — Simons Chern class      345 346
Chen      275
Chern class      338 340
Chudnovsky      1 46 141
Circle method      293
Clausen      8 90 91
Clausen component ladders      91 94
Clausen function      8 15 16 90 92 135 141 239 315 355 358
Clausen function ladders      8 9
Clausen functional equation      84
Clausen ladder      94 95
Cocycle condition      340
Cohen      387 389
Complete system of equivalent points      186 195
Component-ladder      8 35
Congruence      268
Conjecture of Birch and Tate      250
Conjecture of Lichtenbaum      250
Conjecture of Milnor      272
Conjecture on linear independence      391
Coxeter      4 5 11 49 50 52 53 97 99 151 302
Coxeter polytopes      306 321
Coxeter simplexes      322
Cross-ratio      393 394 396
Cyclic symmetry      393
Cyclotomic equation      6 7 20 21 22 24 34 36 39 40 41 42 43 44 54 69 72 74 80 82 90 91 148 154 159 236 288 290 296 365 367
Cyclotomic equations with a factor      264
Cyclotomic polynomial      255
Cyclotomic relation      387
d-truncated orthoschemes      301
Damiano      342
De Doelder      358
de Rham complex      343 351
Dedekind zeta function      xiv 330 377 384
deg f      209
Dehn invariant      331
Deligne      275 383
Deligne cohomology      350
Dependence      254
di-gamma function      355
Dilogarithms      238
Dirichlet L-functions      140 164
Dirichlet L-series      161
Dirichlet theorem      377
dodecahedron      328
Duplication formula      1 29 32 236 240
Dupont      4 5 50 53 333 334 335
Eastham      46
Erdoes — Stewart — Tijdeman      390
Essential      307
Euler      xiii 1 4 5 12 20 36 38 40 287
Euler dilogarithm      238 301 314
Exceptional      256
EXP      213
exp(w)      213
Exponent form      11 117
Factorization formula      154
Factorization theorem      202
Fettis      358
Fifteen-term functional equation      16
Flow chart      39 44 45 52 61 65
Fox H-function      360
Function of Schlaefli      309
Functional equations      28 247 281 340 342 392
Functor of Milnor      233
Fundamental relations      313
G(x)      214 216
G-functions      287
Gangl      xiv 4 6 23 29 39 49 98 151 290 373 374 378 396 398 399
Gauss sum      248
Gelfand — MacPherson higher logarithm      342
General identity for the trilogarithm      141
Generalization of Rogers function      31
Generalized      236
Generalized p-logarithm      351
Generalized Rogers function      34
Generic ladders      34
Generic part of the grassmannian      342
Golden ratio      2
Goncharov      375 382
Good S-units      234
Gordon      297
Gram matrix      304
Haagerup      324
Hain      xiv
Harmonic group      11 28 31 100 105 116
Heptalogarithm      374 384 385
Hexalogarithm      xiv 378 398 399
Higher logarithms      337 341 350
Hilbert’s third problem      331
Hill      3 5 11 18 28 116
Hodge filtration      275 276 277 347
Humbert’s formula      330
Hypergeometric series      292
Hyperlogarithms      171
Ideal points      304
Imaginary part of the dilogarithm      15 16
Inaccessibility      5 6 9 11 110
Inaccessible ladders      23 42 44
INDEX      4
Interated integrals      205
Inversion formula      29 32
Inversion relations      1
Inversion theorem      202
Iterated integral      340
Jensen formula      160
Jorgensen      328
K-theory      xiii xiv 8 373 381
Klein      185
Kneser      301 310
Koelbig      359
Kubert identities      157
Kummer      xiv 3 4 5 6 8 9 11 15 16 27 28 29 39 49 50 71 100 108 151 153 171 185 187 188 190 193 373 375 395
Kummer equations      7 13 15 17 18 19 20 21 33 34 44 54 56 57 62 64 76 80 84 97 102 103 105 107 108 110 114 116 118 334
Kummer formulas      113
Kummer function and its relation to the polylogarithm      27
Kummer functional equation      11 16 37 39 165
Kummer two-variable functional equation      32
Kummer type      12 196
Kummer-type functional equation      186 187 196 203
L-series      161
LADDER      xiii 4 6 387
Ladder clusters      154
Ladder order-independence on reduction of order      33
Ladders from functional equations      21 23
Ladders from quintic equations      24
Ladders on the unit circle      90
Lambert cube      308 311
Landen      xiii 1 2 4 5 12 31 36 38 40 52 287
Lehmer      160
Lerch function      361
Lewin      5 123 124 126 151 152 154 158 161 275 288 291 292 298 378 387
Lichtenbaum      9 92
Linear power relation      123 148 152 165
Ljungren      53
Lobachevsky      301
Lobachevsky function      302 314 315
Logarithm-removal property of Rogers function      20
Logarithmic integral      171
Logarithmic singularity      174
Lorentz space      303
Loxton      5 6 11 22
MacPherson      xiv
Macsyma      28 67 100 101 103 112 121
Mahler measure      123 160 162 164 389
Mantel      17
Max-Planck-Institut fuer Mathematik      xiv
Maximal subscheme      311
Meijer's G-function      360
Mellin transform      359
Meyerhoff      322 330
Milnor conjecture      391
Minimal set      237 251
Mixed Hodge structure      275 276 277
Mixed motives      275
Modified external product      233
Modified function      380
Modified ladder      7
Module $P_{n,k}$      194
Module $P_{n,k}(H_0)$      195
Monodromy group      340
Monodromy of the polylogarithms      279
Monodromy operator      338 339
Multi-variable equation      3
Multiple-angle formulas      18
Multiplication theorem      20
Multivalued Deligne cohomology      346 350
Multivalued Deligne complex      347
Multivalued differential form      343
Multivalued function      340
Munkholm      324
n-dimensional hyperbolic space      303
n-variable identities      124
Nonaccessibility      71
Nonexistence of a Kummer-type functional equation for $Li_6$      197
Nontrivial      236
Nonvalid ladders      70
Notation      6
Order-independence property      7 8
Order-reduction property      7
Ordinary cyclotomic equation      237
Orthoscheme of degree      307
P(X)      212
p-logarithm      343 344
p-logarithm function      344
Partial Clausen's function      241
Partition identities      292
Permanent      305
Phillips      50
Pisot number      160 164 165
Points at infinity      304
Polar hyperplane      304
Polylogarithm extension of Q-mixed Hodge structures      279
Polylogarithm workshop      xiii xiv
Polylogarithms      340
Pontrjagin class      337
Pontryagin classes      275
Principal parameter      311
Principal vertices      307
Pseudodifferentiation      7
Pseudointegrate transparently      52
Pseudointegration      7 35 39 43 46 56 83
Pure form      28
Pure Hodge structure      275 276
Purity property      28 33
Ramakrishnan      141 142
Ramanujan      298
Ray      4 12 29 71 86 90 96 290 292
Real part of the dilogarithm      18
Redefinition of Rogers function      20
Reduction formula      310
Redundant results      78
Regulator      346
Regulator mappings      275
Relation of dependence      251
Richmond      19 292 297 298
Rogers      3 4 8 9 16 28 123 124 287 381 383 385
Rogers dilogarithm      239
Rogers function      7 20 27 28 102 106 110 111 112 117
Rogers — Ramanujan      292 297
Rogers — Ramanujan partition functions      5
Rogers — Ramanujan partition identities      19
Rost      121
S-units      234
Sah      xiv 334 335
Salem      164
Salem number      160 164 364 389
Salem/Pisot numbers      123 160
Sandham      29
Sandham n-variable identity      141
Schaeffer      3 11 28 29 52 116
1 2
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