| Project/Area Number |
22740022
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Chiba Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 概均質ベクトル空間 / ゼータ関数 / 保型超関数 / アイゼンシュタイン級数 / 実解析的保型形式 / b-関数 / リー環 / クイバー |
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| Research Abstract |
We have completed the work on b-functions associated quivers of type A, and published a paper in a journal. Applying a result in the paper, we have obtained some results on functional equations of prehomogeneous vector spaces of parabolic type arising from special linear Lie algebras. Moreover, we have studied the L-functions associated with automorphic distributions defined by Toshiaki Suzuki. As a result, we have observed that the functional equation satisfied by the L-functions associated with automorphic distribution coincides with that satisfied by the L-functions associated with Maass wave forms. Furthemore, we have formulated a converse theorem for automorphic distributions, and combining this with Poisson transforms, we have obtained another proof for the converse theorem for Maass wave forms.
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