Renormalization of Multiple q-Zeta Values
Jianqiang Zhao
Abstract
In this paper we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq(s1,...,sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (math.NT/0606076v3) on the renormalization of Euler-Zagier multiple zeta values. 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 ζq(s1,...,sd) (i.e., s1 1). Moreover, when our renormalizations agree with those of Guo and Zhang.
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