2017 Fiscal Year Final Research Report
Study of independence of periods arising in number theory
| Project/Area Number |
15K17525
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Fukuoka Institute of Technology (2017)
Oyama National College of Technology (2015-2016) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 多重ゼータ値 / 多重ポリログ / 関数体 / 有限多重ゼータ値 / t加群 / 周期 / 線形独立性 / 代数的独立性 |
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| Outline of Final Research Achievements |
In this research, we studied multiple zeta values (MZV's) over the rational function field K over a finite field, and the Carlitz multiple polylogarithms (CMPL's) (joint work with Chieh-Yu Chang). More precisely, we showed that the infinite/v-adic CMPL's are related to some coordinate of the logarithm of an explicitly constructed t-module at a special point, where v is a finite place of K. By using this formula, we proved that an infinite-adic CMPL at an algebraic point is Eulerian if and only if the corresponding v-adic CMPL's at algebraic points are zero. Moreover, we defined v-adic MZV's and proved that v-adic MZV's satisfy the linear relations that their corresponding infinite-adic MZV's satisfy. We also defined finite CMPL's, and showed that each finite MZV over K is a K-linear combination of finite CMPL's at integral points.
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| Free Research Field |
数論
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