Special Values of Multiple Polylogarithms

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.

35 pages

References in corpus (2)

• Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
• On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

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