Multiple zeta values, poly-Bernoulli numbers, and related zeta functions

We study the function ζ(k₁, . . . , k_{n - 1} ; s) = Σ_{0<m1<m2⋯<mn} 1/m^k1₁⋯m^{kn - 1} _{n - 1} m^s_n and show that the poly-Bernoulli numbers introduced in our previous paper are expressed as special values at negative arguments of certain combinations of these functions. As a consequence of our study, we obtain a series of relations among multiple zeta values.