| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Research Abstract |
The Schwarz map for a hypergeometric differential equation of 2 variables induces modular forms on the 2-dimensional complex hyperball. By using these modular forms we obtained
1) Algebraicity criterion for special values of the Schwarz map for a hypergeometric differential equation,
2) Extension in 2 variables of the Gauss arithmetic geometric mean theorem,
3) Extension in 2 variables of the Jacobi theta recursive theorem,
4) Explicit expression of the Shimura curve with discriminant 6.
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