2016 Fiscal Year Final Research Report
Studies on real analytic SIegel modular forms of degree 2--their L-functions and construction
| Project/Area Number |
24740016
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Keywords | 整数論 / 保型形式 / テータ級数 |
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| Outline of Final Research Achievements |
We investigate an old method of constructing the elliptic modular forms as theta series associated with harmonic polynomials from the viewpoint of invariant theory. More precisely, it is easy to see that the space of theta series does not lose any modular fomrs if we restrict the harmonic polynomials invariant under the automorphism group of the lattice involved. We observe that the linear map from O(E_8,Z)-invarinat E_8-harmonic polynomials to the space of elliptic modular forms is injective for small weights. Note that the actual computation is done by Y.Funada, a master course student.
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| Free Research Field |
整数論
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