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Structural Properties of Polylogarithms
 
Edited by: Leonard Lewin
Structural Properties of Polylogarithms
Hardcover ISBN:  978-0-8218-1634-9
Product Code:  SURV/37
List Price: $139.00
MAA Member Price: $125.10
AMS Member Price: $111.20
eBook ISBN:  978-1-4704-1264-7
Product Code:  SURV/37.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Hardcover ISBN:  978-0-8218-1634-9
eBook: ISBN:  978-1-4704-1264-7
Product Code:  SURV/37.B
List Price: $274.00 $206.50
MAA Member Price: $246.60 $185.85
AMS Member Price: $219.20 $165.20
Structural Properties of Polylogarithms
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Structural Properties of Polylogarithms
Edited by: Leonard Lewin
Hardcover ISBN:  978-0-8218-1634-9
Product Code:  SURV/37
List Price: $139.00
MAA Member Price: $125.10
AMS Member Price: $111.20
eBook ISBN:  978-1-4704-1264-7
Product Code:  SURV/37.E
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Hardcover ISBN:  978-0-8218-1634-9
eBook ISBN:  978-1-4704-1264-7
Product Code:  SURV/37.B
List Price: $274.00 $206.50
MAA Member Price: $246.60 $185.85
AMS Member Price: $219.20 $165.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 371991; 412 pp
    MSC: Primary 19; 30; 33; 39; Secondary 11; 51; 57;

    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.

  • Table of Contents
     
     
    • Articles
    • L. Lewin — 1. The evolution of the ladder concept [ MR 1148372 ]
    • L. Lewin — 2. Dilogarithmic ladders [ MR 1148373 ]
    • M. Abouzahra and L. Lewin — 3. Polylogarithmic ladders [ MR 1148374 ]
    • M. Abouzahra and L. Lewin — 4. Ladders in the trans-Kummer region [ MR 1148375 ]
    • M. Abouzahra and L. Lewin — 5. Supernumary ladders [ MR 1148376 ]
    • L. Lewin — 6. Functional equations and ladders [ MR 1148377 ]
    • A. Ray — 7. Multivariable polylogarithm identities [ MR 1148378 ]
    • G. Wechsung — 8. Functional equations of hyperlogarithms [ MR 1148379 ]
    • G. Wechsung — 9. Kummer-type functional equations of polylogarithms [ MR 1148380 ]
    • Zdzisław Wojtkowiak — 10. The basic structure of polylogarithmic equations [ MR 1148381 ]
    • J. Browkin — 11. $K$-theory, cyclotomic equations and Clausen’s function [ MR 1148382 ]
    • Spencer Bloch — 12. Function theory of polylogarithms [ MR 1148383 ]
    • J. H. Loxton — 13. Partition identities and the dilogarithm [ MR 1148384 ]
    • Ruth Kellerhals — 14. The dilogarithm and volumes of hyperbolic polytopes [ MR 1148385 ]
    • Richard M. Hain and Robert MacPherson — 15. Introduction to higher logarithms [ MR 1148386 ]
    • L. Lewin — 16. Some miscellaneous results [ MR 1148387 ]
    • Don Zagier — Appendix A. Special values and functional equations of polylogarithms [ MR 1148388 ]
    • Leonard Lewin — Appendix B. Summary of the informal polylogarithm workshop
  • Reviews
     
     
    • A remarkable book on a remarkable function, brimming with the enthusiasm of new discoveries and ideas for further research.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 371991; 412 pp
MSC: Primary 19; 30; 33; 39; Secondary 11; 51; 57;

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.

  • Articles
  • L. Lewin — 1. The evolution of the ladder concept [ MR 1148372 ]
  • L. Lewin — 2. Dilogarithmic ladders [ MR 1148373 ]
  • M. Abouzahra and L. Lewin — 3. Polylogarithmic ladders [ MR 1148374 ]
  • M. Abouzahra and L. Lewin — 4. Ladders in the trans-Kummer region [ MR 1148375 ]
  • M. Abouzahra and L. Lewin — 5. Supernumary ladders [ MR 1148376 ]
  • L. Lewin — 6. Functional equations and ladders [ MR 1148377 ]
  • A. Ray — 7. Multivariable polylogarithm identities [ MR 1148378 ]
  • G. Wechsung — 8. Functional equations of hyperlogarithms [ MR 1148379 ]
  • G. Wechsung — 9. Kummer-type functional equations of polylogarithms [ MR 1148380 ]
  • Zdzisław Wojtkowiak — 10. The basic structure of polylogarithmic equations [ MR 1148381 ]
  • J. Browkin — 11. $K$-theory, cyclotomic equations and Clausen’s function [ MR 1148382 ]
  • Spencer Bloch — 12. Function theory of polylogarithms [ MR 1148383 ]
  • J. H. Loxton — 13. Partition identities and the dilogarithm [ MR 1148384 ]
  • Ruth Kellerhals — 14. The dilogarithm and volumes of hyperbolic polytopes [ MR 1148385 ]
  • Richard M. Hain and Robert MacPherson — 15. Introduction to higher logarithms [ MR 1148386 ]
  • L. Lewin — 16. Some miscellaneous results [ MR 1148387 ]
  • Don Zagier — Appendix A. Special values and functional equations of polylogarithms [ MR 1148388 ]
  • Leonard Lewin — Appendix B. Summary of the informal polylogarithm workshop
  • A remarkable book on a remarkable function, brimming with the enthusiasm of new discoveries and ideas for further research.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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