2017 Fiscal Year Final Research Report
Number theory for representations of algebraic groups and associated zeta functions
| Project/Area Number |
25707002
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Partial Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kobe University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | ゼータ関数 / 代数群 / 概均質ベクトル空間 / 密度定理 / 指数和 |
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| Outline of Final Research Achievements |
Focusing mainly on zeta functions of prehomogeneous vector spaces, we investigate what kind of zeta functions may be associated with representations of algebraic groups, and their arithmetic significance when they exist. Our primary achievement is an application of density theorems. For counting functions of discriminants of cubic fields, we obtained a strong quantitative result. We also studied exponential sums appearing in the functional equation of the zeta function. We developed a simple and effective method to compute them, and give a variety of new explicit formulas.
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| Free Research Field |
整数論
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