Hermite constants of algebraic groups and their applications
| Project/Area Number |
19540026
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
WATANABE Takao Osaka University, 大学院・理学研究科, 教授 (30201198)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 代数群 / エルミート定数 / ボロノイ理論 / 格子 / 簡約理論 / 格子球充てん問題 / Hermite定数 / Hermite-Rankin定数 / Berge-Martinet定数 / 代数体 / アラケロフ類群 / アラケロフ因子 |
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| Research Abstract |
On the cone of positive definite n by n real symmetric matrices, Hermite's function is defined as a quotient of the arithmetical minimum function and the reduced determinant. The determination of the actual value of the maximum of Hermite's function is equivalent to the determination of the densest lattice sphere packing in an n-dimensional Euclidean space. The local maxima of Hermite's function is characterized by Voronoi's theory. In this research project, we investigated a geometric and arithmetic generalization of Voronoi's theory. We determined exact values of a generalized Hermite constant of a symplectic group and some Rankin -Hermite's constants.
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Report
(4 results)
Research Products
(8 results)
