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Special Values of Multidimensional Polylogarithms

Borwein, Jonathan M. and Bradley, David M. and Broadhurst, David J. and Lisonek, Petr (2001) Special Values of Multidimensional Polylogarithms. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 353 (3). pp. 907-941.

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      Abstract

      Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in combinatorics, knot theory and high-energy physics. More recently, we have been forced to consider multidimensional extensions encompassing the classical polylogarithm, Euler sums, and the Riemann zeta function. Here, we provide a general framework within which previously isolated results can now be properly understood. Applying the theory developed herein, we prove several previously conjectured evaluations, including a longstanding conjecture of Don Zagier.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Euler sums, Zagier sums, multiple zeta values, polylogarithms, multiple harmonic series, quantum field theory, knot theory, Riemann zeta function
      Subjects: 11-xx Number theory > 11Mxx Zeta and $L$-functions: analytic theory
      40-xx Sequences, series, summability > 40Bxx Multiple sequences and series
      33-xx Special functions > 33Exx Other special functions
      11-xx Number theory > 11Yxx Computational number theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 13 Jan 2015 12:22
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/200

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