The structure of a tannakian category formed by equivalence classes of systems of linear inequalities over a number field and its application to diophantine approximation
Project/Area Number |
25400029
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Kanagawa Institute of Technology |
Principal Investigator |
FUJIMORI Masami 神奈川工科大学, 基礎・教養教育センター, 准教授 (20312093)
|
Project Period (FY) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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Keywords | 代数学 / 数論 / ディオファントス近似 / 数体 / 線型不等式 / 淡中圏 / 代数群 / 表現 |
Outline of Final Research Achievements |
It is known that the equivalence classes of systems of linear inequalities which describe a rational approximation property of numbers are naturally identified with the representations of some group. The representative of the present study had in particular shown before via what algebraic group a classical system of linear inequalities which corresponds to the famous Roth inequality is regarded as a representation of the said group. On the other hand, the details of the whole body of the huge group are not very clear yet.
In our present study, we have revealed via what algebraic group a system of linear inequalities which gives a simultaneous rational approximation to a number and to its square is considered a representation of the above-mentioned huge group, leaving aside an exceptional case in a certain sense.
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Report
(4 results)
Research Products
(3 results)