A relation between the various multiple zeta-functions and the hypergeometric function and its application
| Project/Area Number |
15K17517
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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 | Kitasato University (2016-2018)
Nippon Institute of Technology (2015) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 多重ゼータ関数 / 超幾何関数 / 関数等式 / ベルヌーイ多項式 / ルート系のゼータ関数 / 多重ゼータ値 / parity result / クラウゼン関数 |
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| Outline of Final Research Achievements |
The research results of this research are the following two parts.
（1）We gave a relation between the Euler-Zagier multiple zeta-function and the generalized hypergeometric function.
（2）We obtained evaluation formulas between the values of the zeta-functions of the root system of type A2, B2 and G2 for positive integers and the values of Riemann zeta-function and Dirichlet L-function for the positive integer. And also, we gave the relations between the values of the zeta-functions of the root system of type A2 and A3 for positive integers.
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| Academic Significance and Societal Importance of the Research Achievements |
多重ゼータ関数と超幾何関数の関係を用いることで，多重ゼータ関数の関数等式を得られる可能性がある．そして，このように超幾何関数を通して，様々な多重ゼータ関数を捉えることで，様々な多重ゼータ関数に対して有効であるその値の挙動を考察するための研究手法を与えることができる可能性がある．また，ルート系のゼータ関数に関係する多重ゼータ関数の値の挙動の考察を行うことができれば，物理系への応用が期待できる．
また，ルート系のゼータ関数と他の多重ゼータ関数の関係を明らかにすることで，数理物理に関連するある体積の関係を明らかすることができた．
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Report
(5 results)
Research Products
(8 results)
