2000 Fiscal Year Final Research Report Summary
STUDY OF MULTIPLE ZETA VALUES
| Project/Area Number |
10440010
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
KANEKO Masanobu KYUSHU UNIVERSITY, Faculty of Math, Assoc.Prof., 大学院・数理学研究院, 助教授 (70202017)
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| Co-Investigator(Kenkyū-buntansha) |
ARAKAWA Tsuneo Rikkyo Univ, Faculty of Sci.Prof., 理学部, 教授 (60097219)
TAKATA Toshie KYUSHU UNIVERSITY, Faculty of Math, Lecturer, 大学院・数理学研究院, 講師 (40253398)
HANAMURA Masaki KYUSHU UNIVERSITY, Faculty of Math, Assoc.Prof., 大学院・数理学研究院, 助教授 (60189587)
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| Project Period (FY) |
1998 – 2000
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| Keywords | Multiple Zeta Values / Multiple L Values / Multiple Zeta Functions / Poly-Bernoulli numbers |
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| Research Abstract |
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.
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