Renormalization of multiple <Emphasis Type="Italic">q</Emphasis>-zeta values

In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζ _q (s ₁, ..., s _d ) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values, arxiv: math/0606076v3). We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζ _q (s ₁, ..., s _d ) (i.e., s ₁ ≤ 1). Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang.