论文标题
多个Zeta值和迭代的Eisenstein积分
Multiple zeta values and iterated Eisenstein integrals
论文作者
论文摘要
布朗表明，动机路径的辉环Tannakian类别$ \ MATHSF {MT}（\ Mathbb {Z}）$ tate Mathbb {Z} $的混合泰特动机。布朗还引入了多个模块化值，这是Moduli stack $ \ Mathcal {M} _ {1,1} $的基本组相对完成的期间。我们证明，所有动机多个Zeta值都可以表示为$ \ MATHBB {Q} [2πi] $ - 动机迭代的Eisenstein积分沿$π_1（\ Mathcal {m} _ {1,1} _ cong sl_2 feaction femote tho Mathibbb} $ sosition Eisenstein积分的线性组合。这为$ \ mathsf {mt}（\ Mathbb {z}）$提供了一个新的模块化发电机。我们还解释了该线性组合中的系数如何使用动机共同做出部分确定。
Brown showed that the affine ring of the motivic path torsor $π_1^{\text{mot}}(\mathbb{P}^1 \backslash \left\{0,1,\infty\right\}, \vec{1}_0, -\vec{1}_1)$, whose periods are multiple zeta values, generates the Tannakian category $\mathsf{MT}(\mathbb{Z})$ of mixed Tate motives over $\mathbb{Z}$. Brown also introduced multiple modular values, which are periods of the relative completion of the fundamental group of the moduli stack $\mathcal{M}_{1,1}$ of elliptic curves. We prove that all motivic multiple zeta values may be expressed as $\mathbb{Q}[2 πi]$-linear combinations of motivic iterated Eisenstein integrals along elements of $π_1 (\mathcal{M}_{1,1}) \cong SL_2(\mathbb{Z})$, which are examples of motivic multiple modular values. This provides a new modular generator for $\mathsf{MT}(\mathbb{Z})$. We also explain how the coefficients in this linear combination may be partially determined using the motivic coaction.
