Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
arXiv:math/0310061 · doi:10.1023/B:COMP.0000005036.52387.da
Abstract
We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst-Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.
21 pages, To appear in Compositio Mathematica