| Project/Area Number |
18K03233
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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 | University of Tsukuba |
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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 |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 多重ゼータ値 / q類似 / 代数的数 / 有限多重ゼータ値 / 対称多重ゼータ値 / 多重T値 / 多重L値 |
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| Outline of Final Research Achievements |
A q-analogue of a mathematical object is a one-parameter deformation that restores the original object in the limit as the parameter goes to 1. In this study, we investigated a q-analogue of multiple zeta value, which is a multiple sum of negative power of positive integers, and properties of finite multiple sums obtained by specializing the parameter to a root of unity in an appropriate sense. As a result, we clarified the relationship between the finite multiple sums and the Kaneko-Zagier conjecture. We also constructed a new one-parameter deformation of multiple L-value, which is a generalization of the multiple zeta value, with a good algebraic structure. Furthermore, we obtained an expression of the generating function of a variant of the multiple zeta value called multiple T-value.
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| Academic Significance and Societal Importance of the Research Achievements |
Kaneko-Zagier 予想は，素数位数の有限体の元の列である有限多重ゼータ値と，実数である対称多重ゼータ値の間に一対一対応が存在することを主張する。本研究で扱った1のベキ根における有限多重和は，この二つの対象をそれぞれ代数的および解析的な極限操作によって復元する。本研究で得られた成果は，この枠組みを用いてKaneko-Zagier予想を検証するものであり，同予想の解決に向けた新たな視点を提供していると思われる。また，多重ゼータ値の類似物の性質を，特殊関数を用いる初等的な手法によって調べることに成功しており，さまざまな方向への拡張および一般化が期待できる。
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