论文标题
在Euler-Zagier双重Zeta函数的基础上具有非阳性组件
On a basis for Euler-Zagier double zeta functions with non-positive components
论文作者
论文摘要
对于非阴性整数$ n $，令$ \ Mathcal {z} _ {n}：= \ sum^n_ {c = 0} \ mathbb {q} \ cdotζ（-c，-c，s+c）$，右侧是euler-Zag-Zag-Zag-Zag-Zag-Zag-Zag-Zag-Zag $ zeta qusion $ zet $ zeta qutions $ zet $ ketiions qutions $ z。在本文中，我们表明$ \ Mathcal {z} _ {n} = \ bigoplus^{n} _ {c = 0：\ text {fext {fext} \ mathbb {q} \ cdotζ（-c，c，s+c）$，其中$ \ bigoplus $是$ \ bigoplus $属于vector of vector of vector of vector speses。此外，我们给了一个耗尽所有$ \ mathbb {q} $ - $ \ mathcal {z} _ {n} $的线性关系的家庭。
For a non-negative integer $N$, let $\mathcal{Z}_{N}:=\sum^N_{c = 0} \mathbb{Q} \cdot ζ(-c,s+c)$, where the right-hand side is the vector space spanned by the Euler-Zagier double zeta functions over $\mathbb{Q}$. In this paper, we show that $\mathcal{Z}_{N} =\bigoplus^{N}_{c = 0 : \text{even}} \mathbb{Q} \cdot ζ(-c,s+c)$, where $\bigoplus$ is the direct sum of vector spaces. Moreover, we give a family of relations that exhaust all $\mathbb{Q}$-linear relations on $\mathcal{Z}_{N}$.
