Renormalization of Multiple $q$-Zeta Values

Jianqiang Zhao

doi:10.1007/s10114-008-6646-x

Renormalization of Multiple $q$-Zeta Values

数论 2009-07-02 v3

作者: Jianqiang Zhao

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摘要

In this paper we shall define the renormalization of the multiple $q$ -zeta values (M $q$ ZV) which are special values of multiple $q$ -zeta functions $\zeta_q(s_1,...,s_d)$ when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (math.NT/0606076v3) on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process produces the same values if the M $q$ ZVs are well-defined originally and that these renormalizations of M $q$ ZV satisfy the $q$ -stuffle relations if we use shifted-renormalizations for all divergent $\zeta_q(s_1,...,s_d)$ (i.e., $s_1\le 1$ ). Moreover, when $\qup$ our renormalizations agree with those of Guo and Zhang.

关键词

multiple zeta values zeta values and euler sums zeta functions

引用

@article{arxiv.math/0612093,
  title  = {Renormalization of Multiple $q$-Zeta Values},
  author = {Jianqiang Zhao},
  journal= {arXiv preprint arXiv:math/0612093},
  year   = {2009}
}

备注

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 MqZVs

Renormalization of Multiple $q$-Zeta Values

摘要

关键词

引用

备注

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