STUDY OF MULTIPLE ZETA VALUES

多个 Zeta 值的研究

• 批准号: 10440010
• 负责人: KANEKO Masanobu
• 金额: $ 4.29万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10440010/
• 关键词: Multiple Zeta Values; Multiple L Values; Multiple Zeta Functions; Poly-Bernoulli numbers; 結び目不変量

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.

多重zeta值是这些天深入研究的对象。我们特别关注的是找出不同指标值之间的关系，我们建立了一种称为“导子关系”的关系，并证明了它们。这揭示了新的光以前已知的关系“大野关系”。另外，我们还找到了“正则化双洗牌关系”的一个公式，并给出了证明。进一步，我们发现了导子关系与正则化双混洗关系之间的一种关系，得到了支持这一猜想的部分结果。在本项目期间，我们对多重L值以及poly-Bernoulli数和相关的zeta函数做了一些工作。同时，以完备的方式证明了Akiyama-Tanigawa关于计算Bernoulli数的一个很好的算法。

项目成果

Masanobu Kaneko: "When is a polygonal pyramid number again polygonal?"Rockey Mountain J.of Math.. (in press).

Masanobu Kaneko：“多棱锥数什么时候又是多边形的？”Rockey Mountain J.of Math..（正在出版）。

Tsuneo Arakawa: "Multiple zeta values, poly-Bernoulli numbers, and related zeta functions"Nagoya Math.J.. 153. 189-209 (1999)

Tsuneo Arakawa：“多重 zeta 值、聚伯努利数和相关 zeta 函数”Nagoya Math.J.. 153. 189-209 (1999)

Tsuneo Arakawa: "Multinle zeta values, poly-Bernoulli numbers, and related zeta functions"Nagoya Math.J.. 153. 189-209 (1999)

Tsuneo Arakawa：“多重 zeta 值、聚伯努利数和相关 zeta 函数”Nagoya Math.J.. 153. 189-209 (1999)

荒川恒男: "ベルヌーイ数とゼータ関数"牧野書店. 285 (2000)

荒川恒夫：“伯努利数和 zeta 函数”，牧野书店 285 (2000)。

M.Kaneko: "Supersingular J-invariants,hypergeometric series,and Atkin's orthogonal polynomials" AMS/IP Studies in Adv.Math.vol.7. 97-126 (1998)

M.Kaneko：“超奇异 J 不变量、超几何级数和阿特金正交多项式”Adv.Math.vol.7 中的 AMS/IP 研究。