  We first review our previous works of Arakawa and the authors on two, closely
related single-variable zeta functions. Their special values at positive and
negative integer arguments are respectively multiple zeta values and
poly-Bernoulli numbers. We then introduce, as a generalization of Sasaki's
work, level 2 analogue of one of the two zeta functions and prove results
analogous to those by Arakawa and the first named author.
