On the evaluation of multiple zeta values of height one
by
Wen-Chin Liaw
National Chung Cheng University
Coauthors: Minking Eie, Yao Lin Ong.

The multiple zeta values are defined by

z(a1, a2, ..., ar) = å 1 ≤ k1 < k2 < ... < kr  k1-a1 k2-a2 ... kr-ar,

for positive integers a₁, a₂, ..., a_r with a_r ≥ 2.

We shall consider multiple zeta values of height one, i.e., of the form z({1}^p, a), and prove a reduction formula, which enables us to give the explicit evaluation of multiple zeta values of height one and low depth.

Date received: June 13, 2008