| Project/Area Number |
16K05249
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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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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Hosei University (2017-2018)
Utsunomiya University (2016) |
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Principal Investigator |
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| Research Collaborator |
SATO iwao
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | グラフのゼータ関数 / 四元数 / 量子ウォーク / Kirchhoff index / 応用数学 / 代数学 |
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| Outline of Final Research Achievements |
We defined several classes of weighted zeta functions of noncommutative weighted graphs; they are considered to have symmetric directed edges that are weighted by noncommutative quantities such as matrices or quaternions. We obtained main properties of the zeta functions such as determinant expressions. We generalized the theories of first and second weighted zeta functions of graphs to the case of quaternion-weighted graphs and applied them to the analysis of the spectra for quaternionic quantum walks on graphs. We also generalized the theory of first weighted zeta functions to much more general situation that includes the case of quaternions.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究成果は，伊原ゼータ関数に始まるグラフのゼータ関数論を大きく発展させるものであり，四元数量子ウォークへの応用にもみられるように，離散数学，代数学，量子モデルなどへの多大な貢献を期待できる。四元数を初めとする非可換量がグラフ重みとして与えられた場合のゼータ関数のあり方を示したもので，グラフのゼータ関数の非可換化という前人未到のテーマへの礎となるものである。グラフの重み付きゼータ関数がグラフ上の量子ウォークの固有値問題に有効であることから，本研究も量子ウォークとの関連，さらには量子情報などとの関連が期待される。
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