Special Values of Multidimensional Polylogarithms

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 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, a general framework is provided within which previously isolated results can be properly understood. New results and conjectures will also be discussed.