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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
Schematic type      306 310
Scheme      305
Scheme of a polytope      304
Schinzel      158 164
Schlaefli      301
Scissors congruence groups      331
Second-degree ladders      38
Siegel      287
Six-fold symmetry      393
Slater      292 296
Smyth      161
Special exponents      388
Spence      3
Steinberg symbol      233
Stewart      290
Sums      268
Supernumary      12 69
Supernumary component-ladders      38
Supernumary cyclotomic equation      69 78
Supernumary ladders      123 165
Suslin      382
Symmetry group      393 395
Szekeres      19 60 292 293 297 298 370
Tate Hodge structures      276
The Schlaefli differential formula      309
Three-term base equation      12
Three-term equation      24
Three-variable functional equation      17
Thurston      326 328 333
Totally asymptotic regular hexahedron      326
Totally asymptotic regular octahedron      327
Totally asymptotic regular simplex      323
Totally asymptotic simplex      322 334
Trans-Kummer range      31 33 45 49 53 58 61 65 72 97 98 114
Trans-Kummer results      36
Transparency      8 35 70
Transparency property      44
Trivial      12
Tverberg      53
Two-term base equation      11
Two-variable functional equations      29
Type A      308
Type B      308
Unit circle      16
V*      217
Valid ladder      7
Vandiver      155
Vertex polytope      305
Volume differential      301
Volume form      344
Volume spectrum      328
Volumes of hyperbolic 3-folds      328
Watson      5 19 21 22 287 288 291 328
Wechsung      12 17
Weeks manifold      328
Weight filtration      276 277 343
Wigner      333 334
Xiao Hongnian      121
Zagier      xiii xiv 33 61 69 82 92 142 155 275 290 330 365 368
Zeta function      247
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