Sum Relations for Multiple Zeta Values

Abstract

In this note we shall present some identities between sums of multiple zeta values and Riemann zeta values after an overview of our results in [13], [18], [20]. An application of the identities to the Arakawa-Kaneko zeta functions shall also be given. Throughout this note, we shall point out the importance of classifying multiple zeta values by the indices called weight, depth and height, and we shall also indicate the significance of multiple zeta-star values.