2019 Fiscal Year Final Research Report
The outlook for the dimension conjecture and the study of Lie algebras of multiple zeta values and multiple Eisenstein series
Project/Area Number |
18K13393
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Research Category |
Grant-in-Aid for Early-Career Scientists
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Allocation Type | Multi-year Fund |
Review Section |
Basic Section 11010:Algebra-related
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Research Institution | Aichi Prefectural University |
Principal Investigator |
Tasaka Koji 愛知県立大学, 情報科学部, 講師 (30780762)
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Project Period (FY) |
2018-04-01 – 2020-03-31
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Keywords | 多重ゼータ値 / モジュラー形式 |
Outline of Final Research Achievements |
We study a conjecture proposed by Broadhurst and Kreimer in 1997 stating mysterious relationships between multiple zeta values (real numbers) and modular forms (holomorphic function on the complex upper-half plane). One of the upshots of this project is a newly analytic interpretation of the so-called "modular relation (an explicit correspondence between double zeta values and modular forms)", which was first established by Gangl, Kaneko and Zagier in 2006.
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Free Research Field |
整数論
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Academic Significance and Societal Importance of the Research Achievements |
近年,モジュラー関係式を一つの動機として,多重ゼータ値とモジュラー形式を共通の枠組みで捉える研究がヨーロッパを中心にいくつかおこっている。世界的な視点では,むしろ幾何的な方面からのアプローチが盛んであるが,本研究では内在する組合せ的な構造やモジュラー形式の解析理論などに新しい貢献ができたという点において,有意義である。
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