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

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

Cited by in corpus (7)

• Multiple $q$-Zeta Values
• Thirty-two Goldbach Variations
• Duality for Finite Multiple Harmonic q-Series
• Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems
• Evaluations of multiple Dirichlet $L$-values via symmetric functions
• Special Values of Generalized Polylogarithms
• Symmetry results for multiple $t$-values