Polylogarithms and multiple zeta values from free Rota-Baxter algebras
Polylogarithms and multiple zeta values from free Rota-Baxter algebras
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DOI：
10.1007/s11425-010-4044-1
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发表时间：
2010-07
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影响因子：
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通讯作者：
Li Guo;Bin Zhang
中科院分区：
文献类型：
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作者：
Li Guo;Bin Zhang
我们证明了Ihara、Kaneko和Zagier意义下的多对数和正则MZV的Shuffle代数都是具有一个生成元的自由交换非酉Rota-Baxter代数。应用这些结果，我们证明了多对数和正则化的MZV的洗牌关系的全集是由单个级数得到的。我们还采用这种方法研究了MZV的扩展双洗牌关系，将这些洗牌关系与我们以前用重整化方法研究MZV的正则化MZV的准洗牌关系进行了比较。
We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara, Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator. We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series. We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.