Special values of multiple polylogarithms

Oct, 1999
35 pages
Published in:
  • Trans.Am.Math.Soc. 353 (2001) 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 an intriguing conjecture of Don Zagier.
  • euler sums
  • zagier sums
  • multiple zeta values
  • polylogarithms
  • multiple harmonic series
  • quantum field theory
  • knot theory
  • riemann zeta funtion