2012 Fiscal Year Final Research Report
Error terms of density theorems related to prehomogeneous vector spaces
| Project/Area Number |
23654003
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kyoto University (2012)
Tohoku University (2011) |
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Principal Investigator |
YUKIE Akihiko 京都大学, 大学院・理学研究科, 教授 (20312548)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 数論 / 群論 |
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| Research Abstract |
Problems for getting the error term of density theorems related to prehomogeneous vector spaces became clearer. In the quartic case, we have an unpublished result showing a uniform estimate of local orbital integrals. However, in order to use it to reach the error term of the density theorem, more accurate estimate has to be shown to use the inclusion-exclusion principle. For that purpose, we carried out some trial and errors. Also there is some progress in the related local theory on the generalization of the notion of Jordan decomposition.
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