Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
Classical Analysis and ODEs
2007-06-13 v1 Number Theory
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.
Cite
@article{arxiv.math/0310061,
title = {Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth},
author = {Douglas Bowman and David M. Bradley},
journal= {arXiv preprint arXiv:math/0310061},
year = {2007}
}
Comments
21 pages, To appear in Compositio Mathematica