Project/Area Number |
16K17583
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Osaka Institute of Technology |
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)
|
Project Period (FY) |
2016-04-01 – 2019-03-31
|
Project Status |
Completed (Fiscal Year 2018)
|
Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
Keywords | 多重ゼータ値 / 多重ベルヌーイ数 / 有限多重ゼータ値 / 数論 |
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.
|
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.
|