Relations of multiple zeta values and their algebraic expression

2000/10/13 by Michael E. Hoffman, Yasuo Ohno · 2 citations
Mathematics · #math.QA #msc:16W30 #msc:11M06 #msc:16W25

paper · pdf

published as J. Algebra 262 (2003), 332-347 · 14 pages AMS-TeX

arxiv created 2000/10/13 · arxiv updated 2009/11/30

Abstract

We establish a new class of relations among the multiple zeta values ζ(k₁,k₂,...,k_n), which we call the cyclic sum identities. These identities have an elementary proof, and imply the "sum theorem" for multiple zeta values. They also have a succinct statement in terms of "cyclic derivations" as introduced by Rota, Sagan and Stein. In addition, we discuss the expression of other relations of multiple zeta values via the shuffle and "harmonic" products on the underlying vector space H of the noncommutative polynomial ring Q<x,y>, and also using an action on Q<x,y> of the Hopf algebra of quasi-symmetric functions.

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• Derivative Sums of Balanced Gamma Quotients and Multiple Zeta Values: Five Conjectures of Zhi-Wei Sun
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