Borwein, Jonathan M. and Bradley, David M. and Broadhurst, David J. and Lisonek, Petr (1998) Special Values of Multidimensional Polylogarithms. [Preprint]
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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 a longstanding conjecture of Don Zagier.
| Item Type: | Preprint |
|---|---|
| Additional Information: | pubdom FALSE |
| Uncontrolled Keywords: | Euler sums, Zagier sums, multiple zeta values, polylogarithms, multiple harmonic series, quantum field theory, knot theory, Riemann zeta function |
| Subjects: | 11-xx Number theory > 11Mxx Zeta and $L$-functions: analytic theory 40-xx Sequences, series, summability > 40Bxx Multiple sequences and series 33-xx Special functions > 33Exx Other special functions 11-xx Number theory > 11Yxx Computational number theory |
| Divisions: | UNSPECIFIED |
| Depositing User: | Users 1 not found. |
| Date Deposited: | 28 Nov 2003 |
| Last Modified: | 21 Apr 2010 11:13 |
| URI: | http://docserver.thecarma.com/id/eprint/200 |
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