STUDY OF MULTIPLE ZETA VALUES

多重Zeta值是这些天来深入研究的对象。特别关注的是寻找不同指标的价值之间的关系。我们提出了一种这样的关系，称为派生关系，并对其进行了证明。这为以前所知的关系“Ohno关系”提供了新的线索。此外，我们还找到了“正则化双洗牌关系”的公式，并给出了证明。在此基础上，我们发现了导数关系与正则化的双洗牌关系之间的猜想关系，并得到了支持该猜想的部分结果。在本项目期间，我们对多重L值以及多项伯努利数和相关的Zeta函数做了一些工作。此外，还证明了Akiyama-Tanigawa计算Bernoulli数的一个很好的算法。

Multiple zeta values is an object of intensive study these days. Particularly concerned is to find relations among values of different indices.We have formulated one of such relations called "derivation relations", and proved them. This sheds new light on the previously known relations "Ohno relations". Also, we found a formulation of "regularized double shuffle relations" and gave a proof. Further, we found a conjectural relationship between the derivation relations and the regularized double shuffle relations and obtained a partial result which supports the conjecture.Some works on the multiple L values, as well as on poly-Bernoulli numbers and related zeta functions, have been done during the period of this project. Also, a nice algorithm of Akiyama-Tanigawa on computing Bernoulli numbers is proved in a self-contained manner.