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For k ≤ n, let E(mn, k) be the sum of all multiple zeta values of depth k and weight mn with arguments are multiples of m ≥ 2. More precisely, E(mn, k) = |α|=n ζ(mα 1 , mα 2 , . . . , mα k ). In this paper, we develop a formula to express E(mn, k) in terms of ζ({m} p ) and ζ ⋆ ({m} q ), 0 ≤ p, q ≤ n. In particular, we settle Genčev's conjecture on the evaluation of E(4n, k) and also evaluate E(mn, k) explicitly for small even m ≤ 8.

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In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple t-values t(α) and define similarly the multiple star t-values as t ⋆ (α). Then we consider the sum of all such multiple (star) t-values of fixed depth and weight with even argument and prove that such a sum can be evaluated when the evaluations of t({2m} n ) and t ⋆ ({2m} n ) are clear. We give the evaluations of them in terms of the classical Euler numbers through their generating functions.

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