- Title
- Special values of multiple polylogarithms
- Creator
- Borwein, Jonathan M.; Bradley, David M.; Broadhurst, David J.; Lisoněk, Petr
- Relation
- Transactions of the American Mathematical Society Vol. 353, Issue 3, p. 907-941
- Publisher Link
- http://dx.doi.org/10.1090/S0002-9947-00-02616-7
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 2001
- Description
- Historically, the polylogarithm has attracted specialists and nonspecialists 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.
- Subject
- Euler sums; Zagier sums; multiple zeta values; polylogarithms; multiple harmonic series; quantum field theory; knot theory; Riemann zeta function
- Identifier
- http://hdl.handle.net/1959.13/940408
- Identifier
- uon:12998
- Identifier
- ISSN:0002-9947
- Rights
- First published in Transactions of the American Mathematical Society in Vol. 353, No. 3, pp. 907-941, 2001, published by the American Mathematical Society.
- Language
- eng
- Full Text
- Reviewed
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