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Renormalization of Multiple -Zeta Values
In this paper we shall define the renormalization of the multiple -zeta
values (MZV) which are special values of multiple -zeta functions
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 MZVs are well-defined originally and that these renormalizations of
MZV satisfy the -stuffle relations if we use shifted-renormalizations for
all divergent (i.e., ). Moreover, when \qup
our renormalizations agree with those of Guo and Zhang.Comment: 22 pages. This is a substantial revision of the first version. I
provide a new and complete proof of the fact that our renormalizations
satisfy the q-stuffle relations using the shifting principle of MqZV