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arXiv:math/0310062 [math.CA]AbstractReferencesReviewsResources

Multiple Polylogarithms: A Brief Survey

Douglas Bowman, David M. Bradley

Published 2003-10-05Version 1

We survey various results and conjectures concerning multiple polylogarithms and the multiple zeta function. Among the results, we announce our resolution of several conjectures on multiple zeta values. We also provide a new integral representation for the general multiple polylogarithm, and develop a q-analogue of the shuffle product.

Comments: 22 pages, in "Proceedings of a Conference on q-Series with Applications to Combinatorics, Number Theory and Physics," (Bruce C. Berndt and Ken Ono eds.) American Mathematical Society, Contemporary Mathematics, Vol. 291, 2001, pp. 71-92. [MR #2003c:33021]
Journal: pp. 71--92 in "q-series with applications to combinatorics, number theory, and physics" (Urbana, Illinois, 2000), Contemporary Mathematics Vol. 291, American Mathematical Society, Providence, Rhode Island, 2001. MR1874522 (2003c:33021)
Categories: math.CA, math.NT
Subjects: 33E20, 11G55, 11M99, 40B05
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