Structural properties of polylogarithms / Leonard Lewin, editor.

Format:

Book

Contributor:

Lewin, Leonard, 1919- editor.

Series:

Mathematical surveys and monographs ; v. 37.

Mathematical surveys and monographs, 0076-5376 ; volume 37

Language:

English

Subjects (All):

Logarithmic functions.

Physical Description:

1 online resource (432 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1991]

Language Note:

English

Summary:

About ten years ago, the handful of peculiar numerical diogarithmic 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.

Contents:

""Contents""; ""Preface""; ""Acknowledgments""; ""List of Contributors""; ""Chapter 1. The Evolution of the Ladder Concept""; ""1.1 Early History""; ""1.2 Functional Equations""; ""1.3 More Recent Numerical Results""; ""1.4 Current Developments""; ""1.5 Base on the Unit Circle and Clausen Function Ladders""; ""References""; ""Chapter 2. Dilogarithmic Ladders""; ""2.1 Derivation from Kummer's Functional Equation""; ""2.2 Relation to Clausen's Function""; ""2.3 A Three-Variable Dilogarithmic Functional Equation""; ""2.4 Functional Equations in the Complex Plane""

""5.4 Supemumary Results for p = 6""""5.5 Supemumary Results for the Equation-family u[sup(6m+1)] + u[sup(6r-1)] = 1""; ""5.6 Supemumary Results for an Irreducible Quintic""; ""5.7 Supemumary Ladders from a 15-Term Functional Equation""; ""5.8 Supemumary Ladders on the Unit Circle""; ""References""; ""Chapter 6. Functional Equations and Ladders""; ""6.1 New Categories of Functional Equations""; ""6.2 The p-family of Equations""; ""6.3 The ω-family of Equations""; ""6.4 The Θ-family of Equations""; ""Acknowledgements""; ""References""; ""Chapter 7. Multivariable Polylogarithm Identities""

""7.0 Introduction""""7.1 A General Identity for the Dilogarithm""; ""7.2 A General Identity for the Bloch-Wigner Function""; ""7.3 A General Identity for the Trilogarithm and D[sub(3)](z)""; ""7.4 Linear Power Relations among Dilogarithms""; ""7.5 Cyclotomic Equations and Bases for Polylogarithm Relations""; ""7.6 Mahler's Measure and Salem/Pisot Numbers""; ""7.7 Recent Results for Supemumary Ladders""; ""References""; ""Chapter 8. Functional Equations of Hyperlogarithms""; ""8.1 Hyperlogarithms""; ""8.2 Logarithmic Singularities""; ""8.3 The Linear Spaces LI[sub(n)] and PLI[sub(n)]""

""8.4 Functional Equations of Hyperlogarithms""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 405-408) and index.

Description based on print version record.

ISBN:

1-4704-1264-0