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 no...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 （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 ζq（S1,..., sd） （i.e., s1 ≤ 1）. Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang.展开更多
文摘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 （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 ζq（S1,..., sd） （i.e., s1 ≤ 1）. Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang.
