STUDY OF MULTIPLE ZETA VALUES

多个zeta值是目前深入研究的对象。特别关注的是找出不同指标之间的关系。我们表述了其中一种称为“派生关系”的关系，并证明了它。这为以前已知的关系“大野关系”提供了新的线索。此外，我们还找到了“正则化双洗牌关系”的一个表述，并给出了证明。进一步，我们在推导关系和正则化双洗牌关系之间建立了一个推测关系，并得到了支持该推测的部分结果。在这个项目期间，已经做了一些关于多重L值的工作，以及关于聚伯努利数和相关的zeta函数的工作。此外，还以自包含的方式证明了Akiyama-Tanigawa计算伯努利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.