Structural Properties of Polylogarithms

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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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Editorial Reviews

Booknews
The pace of new research has been rapid, and the editor has endeavored to keep the book's contents up-to-date by the last minute inclusion of two appendices--one on a special workshop on polylogarithms held in November 1990, and one on recent discoveries on the relation of functional equations to polylogarithmic ladders, Dedekind's zeta function--and inclusion of the recent discovery of a two-variable functional equation for the hexalogarithm, which is the first significant advance in the area in 150 years. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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