Berndt, Bruce C. (ed.) et al., -series with applications to combinatorics, number theory, and physics. Proceedings of a conference, University of Illinois, Urbana-Champaign, IL, USA, October 26-28, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 291, 71-92 (2001).
The multiple polylogarithm is defined by
where and are complex numbers suitably restricted so that the sum converges. When , the multiple polylogarithm reduces to a multiple zeta function
As the title of the paper indicates, a survey of many results and conjectures for multiple polylogarithms and multiple zeta functions is given. Generally, proofs do not appear here, but an extensive list of references is provided. A new integral representation for the multiple polylogarithm is given, and a -analogue of the shuffle product is developed.