2018 Fiscal Year Final Research Report
Relations of finite multiple polylogarithms and finite multiple zeta values
| Project/Area Number |
16K17583
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka Institute of Technology |
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Principal Investigator |
Kamano Ken 大阪工業大学, ロボティクス&デザイン工学部, 准教授 (50409611)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 多重ゼータ値 / 多重ベルヌーイ数 |
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| Outline of Final Research Achievements |
By using the shuffle relation of finite multiple zeta values, new relations of finite multiple zeta values are obtained . As a special case, this relation gives a certain weighted sum formula for finite multiple zeta values.
A generating function of the number of Lonesum decomposable matrices is explicitly given, and its properties in modulo primes p are also given.
Matiyasevich type formula, which is a convolution formula, for poly-Bernoulli numbers and polynomials are obtained.
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| Free Research Field |
数論
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| Academic Significance and Societal Importance of the Research Achievements |
証明した有限多重ゼータ値の公式は，有限多重ゼータ値が興味深い代数的構造を持つことを示しており，有限多重ゼータ値の今後のさらなる研究の進展に期待できる．
ロンサム分解可能行列は組合せ論的な対象であり，代数的・解析的な側面の多い多重ゼータ値の分野において，新しい見方を提供した．
多重ベルヌーイ数は多重ゼータ値と関係が深く，自明には得られない畳み込み関係式を今回得たことにより，多重ベルヌーイ数がとても素性のよいものであることが示された．
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