  In this paper we shall define a special-valued multiple Hurwitz zeta
functions, namely the multiple $t$-values $t(\boldsymbol{\alpha})$ and define
similarly the multiple star $t$-values as $t^{\star}(\boldsymbol{\alpha})$.
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 $t^{\star}(\{2m\}^n)$ are clear. We give
the evaluations of them in terms of the classical Euler numbers through their
generating functions.

Number Theory