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

2003/10/01 by Douglas Bowman, David M. Bradley · 4 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.CA #math.NT #msc:11G55 #msc:33C05 #msc:33E20

paper · pdf · doi:10.1023/b:comp.0000005036.52387.da

published as Compositio Mathematica, Vol. 139, Issue 1, October 2003, pp. 85--100. MR2024966 (2005f:11196) · 21 pages, To appear in Compositio Mathematica

openalex publication_date 2003/10/01 · arxiv created 2003/10/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

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.

Cited by

• Multiple q-zeta values
• Duality for finite multiple harmonic q-series
• THIRTY-TWO GOLDBACH VARIATIONS
• Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems