论文标题
评估多个Zeta值$ζ（2，\ ldots，2,4,2，\ ldots，2）$和周期多项式关系
Evaluation of the multiple zeta values $ζ(2,\ldots,2,4,2,\ldots,2)$ and period polynomial relations
论文作者
论文摘要
在研究多个Zeta值的深度过滤时，由于IT与珊瑚滤过的差异，很快就会出现困难。特别是，深度为$ sl_2（\ mathbb {z}）$的深度分级代数有其他关系。相比之下，已知块过滤是一种简单的组合过滤，与珊瑚过滤相一致，因此相关分级没有类似的缺陷。但是，通过对$ζ的明确评估（2，\ ldots，2,4,2，\ ldots，2）$作为双重Zeta值的多项式，我们得出了这些时期的多项式关系，这是由于在块中衍生出多个Zeta的block Quite froun for double Zetal forder for Boudle Zeta的galoiis Zeta fortile Zeta fortile Zeta的固有符号的结果。然后，我们将其应用于经典双重Zeta值的多个$ t $ t（2 \ ell，2k）$的评估。
In studying the depth filtration on multiple zeta values, difficulties quickly arise due to a disparity between it and the coradical filtration. In particular, there are additional relations in the depth graded algebra coming from period polynomials of cusp forms for $SL_2(\mathbb{Z})$. In contrast, a simple combinatorial filtration, the block filtration is known to agree with the coradical filtration, and so there is no similar defect in the associated graded. However, via an explicit evaluation of $ζ(2,\ldots,2,4,2,\ldots,2)$ as a polynomial in double zeta values, we derive these period polynomial relations as a consequence of an intrinsic symmetry of block graded multiple zeta values in block degree 2. In deriving this evaluation, we find a Galois descent of certain alternating double zeta values to classical double zeta values, which we then apply to give an evaluation of the multiple $t$ values $t(2\ell,2k)$ in terms of classical double zeta values.
