A note on ${\mathcal{F}}_n$-multiple zeta values

Abstract

For several evaluations of special values and several relations known only in ${\mathcal{A}}_n$-multiple zeta values or ${\mathcal{S}}_n$-multiple zeta values, we prove that they are uniformly valid in ${\mathcal{F}}_n$-multiple zeta values for both the case where $\mathcal{F}=\mathcal{A}$ and $\mathcal{F}=\mathcal{S}$. In particular, the Bowman-Bradley type theorem and sum formulas for ${\mathcal{S}}_2$-multiple zeta values are proved.

27 pages, to appear in Commentarii mathematici Universitatis Sancti Pauli