2015 Fiscal Year Final Research Report
Zeta functions of prehomogeneous vector spaces and automorphic distributions
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 |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Chiba Institute of Technology |
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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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) |
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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Free Research Field |
代数学
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