Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

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dc.creatorBowman, Douglas
dc.creatorBradley, David M.
dc.date2003-10-05
dc.date.accessioned2026-07-07T08:06:10Z
dc.date.available2026-07-07T08:06:10Z
dc.descriptionWe 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.
dc.description21 pages, To appear in Compositio Mathematica
dc.identifierhttps://arxiv.org/abs/math/0310061
dc.identifierhttp://arxiv.org/abs/math/0310061
dc.identifierCompositio Mathematica, Vol. 139, Issue 1, October 2003, pp. 85--100. MR2024966 (2005f:11196)
dc.identifierdoi:10.1023/B:COMP.0000005036.52387.da
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130516
dc.subjectClassical Analysis and ODEs
dc.subjectNumber Theory
dc.subject33E20 (Primary) 33C05, 11G55 (Secondary)
dc.titleResolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
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