Relations of multiple zeta values and their algebraic expression

Details Relations of multiple zeta values and their algebraic expression Relations of multiple zeta values and their algebraic expression

2000-10-13

arxiv.org/abs/math/0010140v1

J. Algebra 262 (2003), 332-347

Mathematics

Quantum Algebra

14 pages AMS-TeX

Scientific paper

We establish a new class of relations among the multiple zeta values \zeta(k_1,k_2,...,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, and also using an action on Q of the Hopf algebra of quasi-symmetric functions.

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