| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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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