论文标题
$μ_2，μ_3$和$μ_4$的单元环数多重Zeta值
Unit cyclotomic multiple zeta values for $μ_2,μ_3$ and $μ_4$
论文作者
论文摘要
用$ε$表示$ n^{th} $ unity的原始根。在本文中，我们表明，$μ_n$的单位循环多Zeta值在$ n = 2,3,4 $的情况下生成了$μ_n$的所有环形多Zeta值。此外，$μ_n$的单位环体多ZETA值可以写为$ \ MATHBB {Q} $ - $ \ left的线性组合（ζ\ binom {1}ε\ right）^n，\ lest（emom {binom {binom {1}如果有$ n = 2,3 $和$ 4 $。通过对动机Galois动作的详细分析，我们计算了$ \ left的系数（ζ\ binom {1}ε\ right）^n，\ left（ζ\ binom {1} {ε^{ - ε^{ - 1}}}}} \ right）^n $在上面的单位单位cyclotsclotsclotsclotsclotsclotsclotip zeta的表达式中。
Denote by $ε$ a primitive root of $N^{th}$-unity. In this paper, we show that the unit cyclotomic multiple zeta values for $μ_N$ generate all the cyclotomic multiple zeta values for $μ_N$ in cases $N=2,3,4$. Moreover, the unit cyclotomic multiple zeta values for $μ_N$ can be written as $\mathbb{Q}$-linear combinations of $\left(ζ\binom{1}ε\right)^n, \left(ζ\binom{1}{ε^{-1}}\right)^n$ and lower depth terms in each weight $n$ in case of $N=2,3$ and $4$. By detailed analysis of the motivic Galois action, we compute the coefficients of $\left(ζ\binom{1}ε\right)^n, \left(ζ\binom{1}{ε^{-1}}\right)^n$ in the above expressions of unit cyclotomic multiple zeta values.
