ENGLISH

Structural properties of polylogarithms

By Leonard Lewin

Book information

Publisher
American Mathematical Society
Year
1991
ISBN
0821816349, 9780821816349
ISSN
0076-5376
LCC
QA342 .S77 1991
Open Library ID
OL1539630M
Language
english
Format
DJVU
Filesize
5 MB (5433512 bytes)
Series
Mathematical surveys and monographs 37
Pages
214\214
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

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.

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