Special values of multiple polylogarithms
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Publication:4523172
DOI10.1090/S0002-9947-00-02616-7zbMATH Open1002.11093arXivmath/9910045OpenAlexW1827962746WikidataQ56287593 ScholiaQ56287593MaRDI QIDQ4523172
Author name not available (Why is that?)
Publication date: 8 January 2001
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/math/9910045
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