2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130517We 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.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]Classical Analysis and ODEsNumber Theory33E20 (Primary) 11G55, 11M99, 40B05 (Secondary)text