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Special values of multiple polylogarithms

Borwein, Jonathan M.; Bradey, David M.; Broadhurst, David J. and Lisonek, Petr (2001). Special values of multiple 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 an intriguing conjecture of Don Zagier.

Item Type: Journal Article
ISSN: 0002-9947
Academic Unit/Department: Science > Physical Sciences
Item ID: 9651
Depositing User: David Broadhurst
Date Deposited: 03 Oct 2007
Last Modified: 05 Dec 2010 06:04
URI: http://oro.open.ac.uk/id/eprint/9651
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