On the relation between infinite and finite places from the viewpoint of multiple zeta values over function fields
| Project/Area Number |
18K13398
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | University of the Ryukyus (2019-2022)
Fukuoka Institute of Technology (2018) |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 多重ゼータ値 / 関数体 / 周期 / t加群 / tモチーフ / 線型独立性 / Carlitz多重ポリログ / 正標数 / 数論 |
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| Outline of Final Research Achievements |
We studied infinite/v-adic multiple zeta values over function fields in positive characteristic, where v is a finite place of the function field. More precisely, we proved that the v-adic multiple zeta values satisfy the same algebraic relations that their corresponding infinite-adic multiple zeta values satisfy (joint work with Chieh-Yu Chang and Yen-Tsung Chen). We also studied the structure of the t-module, which is important in the above proof (joint work with Chang and Nathan Green). In addition, we determined the basis of the space of infintie-adic multiple zeta values (joint work with Chang and Chen).
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| Academic Significance and Societal Importance of the Research Achievements |
無限進多重ゼータ値の間の代数的関係式がv進多重ゼータ値に伝播するという結果は，その証明手法が新しく，様々な拡張や応用があると考えられる．また，無限進多重ゼータ値が張る空間の基底の決定は，本分野における中心的な課題の一つであった．本結果により，無限進多重ゼータ値への理解が大きく進展したと考えられる．これらの結果の標数0における類似の問題は未解決であり，本研究の結果や証明の手法が，標数0への良い影響を与えると期待している．
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Report
(6 results)
Research Products
(26 results)
