ANALYTIC CONTINUATION OF MULTI-VARIABLE ARAKAWA-KANEKO ZETA FUNCTION FOR POSITIVE INDICES AND ITS VALUES AT POSITIVE INTEGERS

摘要

We consider a multi-variable generalization of the zeta function defined by Arakawa and Kaneko. We establish its analytic continuation to an entire function, whence it follows that values at non-positive integers are expressed as multi-indexed poly-Bernoulli numbers of C-type. We also prove that its values at positive integers are in the space spanned by multiple zeta values.