2009 Fiscal Year Final Research Report
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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| Keywords | 代数群 / エルミート定数 / ボロノイ理論 / 格子 / 簡約理論 |
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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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