Gamma series associated to elements satisfying regularized double shuffle relations
Gamma series associated to elements satisfying regularized double shuffle relations
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DOI：
10.1016/j.jnt.2009.08.010
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发表时间：
2010-02
影响因子：
0.7
通讯作者：
Zhonghua Li
中科院分区：
文献类型：
--
作者：
Zhonghua Li
设K是特征为0的域，R是交换K-代数。设Φ（x 0，x1）是R《x 0，x1》中具有正则化双洗牌关系的元素。定义了一个与Φ相联系的伽玛级数ΓΦ（s）∈1+ s2 R [s].证明了相应的beta级数是交换形式幂级数环R[x 0，x1]中ΦY（x 0，x1）的象，其中若Φ=1+Φ 0x 0 +Φ 1x 1，则ΦY=1+Φ 1x 1.给出了伽玛级数ΓΦ（s）的反射公式的一些等价条件.
Let K be a field of characteristic 0, and R be a commutative K-algebra. Let Φ(x0,x1) be an element in R《x0,x1》 with regularized double shuffle relations. We define a gamma series ΓΦ(s)∈1+s2R[s] associated to Φ. We prove that the associated beta series is just the image of ΦY(x0,x1) in the commutative formal power series ring R[x0,x1], where if Φ=1+Φ0x0+Φ1x1, then ΦY=1+Φ1x1. We also give some equivalent conditions for the reflection formula of the gamma series ΓΦ(s).