Iterated integrals on P1\{0, 1, ∞, z} and a class of relations among multiple zeta values
Iterated integrals on P1\{0, 1, ∞, z} and a class of relations among multiple zeta values
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P1{0, 1, ∞, z} 上的迭代积分以及多个 zeta 值之间的一类关系
DOI：
10.1016/j.aim.2019.03.005
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发表时间：
2019
影响因子：
1.7
通讯作者：
Nobuo Sato
中科院分区：
文献类型：
--
作者：
Minoru Hirose;Nobuo Sato
本文考虑了P_1∖{0，1，∞，z}上的迭代积分，定义了它们之间的一类q-线性关系，这种关系源于迭代积分关于z的微分结构，然后我们通过取z-→1的极限来定义多个zeta值之间的一类新的q-线性关系，我们称之为合流关系(即由两个穿孔点的合流得到的关系)。汇合关系的意义之一是它给了一个富裕的家庭，似乎耗尽了多重Zeta值之间的所有线性关系。作为一个很好的理由，我们证明了汇合关系既包含正则化的双重洗牌关系，也包含对偶关系。
In this paper we consider iterated integrals on P 1∖{0, 1,∞, z} and define a class of Q-linear relations among them, which arises from the differential structure of the iterated integrals with respect to z. We then define a new class of Q-linear relations among the multiple zeta values by taking their limits of z→ 1, which we call confluence relations (ie, the relations obtained by the confluence of two punctured points). One of the significance of the confluence relations is that it gives a rich family and seems to exhaust all the linear relations among the multiple zeta values. As a good reason for this, we show that confluence relations imply both the regularized double shuffle relations and the duality relations.