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

Abstract

We study the function $$\zeta(k_1,\dots,k_{n-1};s)=\sum_{0<m_1<m_2<\cdots<m_n}\frac{1}{m_1^{k_1}\cdots m_{n-1}^{k_{n-1}}m_n^{s}}$$ 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.