2021 Fiscal Year Final Research Report
Research on analytic functions of several complex variables appearing in number theory
| Project/Area Number |
18K03218
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | 整数論 / ゼータ関数 |
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| Outline of Final Research Achievements |
In this study, we aim to consider the properties of zeta functions which play important roles in the research of Number Theory. In particular, based on the study of E. Witten who is the famous researcher of Mathematical physics, we studied Witten's zeta function. Also we studied Arakawa-Kaneko zeta functions which include polylogarithms and gave new results, in particular new explicit expressions of the special values of these functions, which are important in this area. These results have been recently studied by a lot of researchers. Further development of this research can be expected in the near future.
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| Free Research Field |
代数学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の成果は, これまでの研究で得られていた結果を一般的に扱っているという点で重要なものであると考えられる. これまで個別に研究されていたEuler-Zagier型, Mordell-Tornheim型, Apostol-Vu型などと呼ばれる多重級数型のゼータ関数が, 様々な研究者によって個別に研究されてきたが, 多変数Wittenゼータ関数という広いクラスの研究を行うことで, 既知の結果の統一的な考察, さらには今後の研究すべき方向性が統一的に見通せるという意味で, 非常に重要な視点を与えていると考えられる.
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