| Project/Area Number |
25400021
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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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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| Co-Investigator(Renkei-kenkyūsha) |
Sato Fumihiro 立教大学, 名誉教授 (20120884)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 概均質ベクトル空間 / ゼータ関数 / 保型超関数 / 実解析的保型形式 / 国際研究者交流（フランス） |
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| Outline of Final Research Achievements |
We have studied automorphic distributions. We have proved a converse theorem by which one can construct automorphic distributions for congruence subgroups from L-functions with functional equations, and by using the Poisson transform, we have established a method to construct real analytic automorphic forms for congruence subgroups from L-functions. Moreover, we have confirmed that a certain prehomogeneous zeta function with 2 variables, which has been studied by Takahiko Ueno, satisfies the assumption of our converse theorem. This gives Maass forms whose coefficients are the number of the solutions of quadratic congruence equations.
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