Structural properties of polylogarithms
著者
書誌事項
Structural properties of polylogarithms
（Mathematical surveys and monographs, v. 37）
American Mathematical Society, c1991
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
The evolution of the ladder concept by L. Lewin Dilogarithmic ladders by L. Lewin Polylogarithmic ladders by M. Abouzahra and L. Lewin Ladders in the trans-Kummer region by M. Abouzahra and L. Lewin Supemumary ladders by M. Abouzahra and L. Lewin Functional equations and ladders by L. Lewin Multivariable polylogarithm identities by G. A. Ray Functional equations of hyperlogarithms by G. Wechsung Kummer-type functional equations of polylogarithms by G. Wechsung The basic structure of polylogarithmic functional equations by Z. Wojtkowiak $K$-theory, cyclotomic equations, and Clausen's function by J. Browkin Function theory of polylogarithms by S. Bloch Partition identities and the dilogarithm by J. H. Loxton The dilogarithm and volumes of hyperbolic polytopes by R. Kellerhals Introduction to higher logarithms by R. M. Hain and R. MacPherson Some miscellaneous results by L. Lewin Appendix A: Special values and functional equations of polylogarithms by D. Zagier Appendix B: Summary of the informal polylogarithm workshop by R. MacPherson and H. Sah.
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