| 研究課題/領域番号 |
23K03030
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分11010:代数学関連
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| 研究機関 | 名古屋大学 |
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研究代表者 |
BACHMANN Henrik 名古屋大学, 多元数理科学研究科, 准教授 (20813372)
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| 研究期間 (年度) |
2023-04-01 – 2026-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
3,640千円 (直接経費: 2,800千円、間接経費: 840千円)
2025年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
2024年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
2023年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
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| キーワード | multiple zeta values / Eisenstein series / modular forms / q-analogues of MZV |
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| 研究開始時の研究の概要 |
This research projects deals with the modular phenomena for finite multiple zeta values. This project is motivated by the Kaneko-Zagier which predicts an explicit connection of classical multiple zeta values, for which some modular phenomena can be explained, and their finite analogues.
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| 研究実績の概要 |
In this year, I finished the project "Formal multiple Eisenstein series and their derivations" in joint work with Jan-Willem van Ittersum. In this work we introduce formal multiple Eisenstein series as a formal analogue for multiple Eisenstein series. This can be seen as a natural analog of formal multiple zeta values, which are constructed as formal symbols satisfying the extended double shuffle relations. The main result of this project is that we show that the algebra of formal multiple Eisenstein series as the structure of an sl2-algebra, generalizing the sl2-structure of quasimodular forms in a natural way. Besides this, I started another project on formal finite multiple zeta values and on the algebraic structure of certain q-analogues.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The work on formal multiple Eisenstein series was finally finished positively after almost 3 years. It was presented by me at several conferences abroad and also domestically.
The new project on formal finite multiple zeta values is going smoothly, and me and my collaborator (Risan, Nagoya University) have already obtained several new results. We still have a lot of open questions we want to address, but are doing steady progress on them.
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| 今後の研究の推進方策 |
Besides the above-mentioned projects, I am currently also discussing a possible further project with Tadashi Okazaki on the connection to physics. Besides this I am planning to give several talks this year on the ongoing projects on formal finite multiple zeta values. The first one will be at a conference in China in June. In the summer, I am planning to organize a mini workshop on q-analogs of multiple zeta values in Hamburg, Germany. There, I will also meet some of my former collaborators to discuss further possible projects.
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