2010 Fiscal Year Final Research Report
Arithmetic relations between modular forms and hypergeometric functions in several variables
| Project/Area Number |
20540007
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
SIGA Hironori Chiba University, 理工学術院, 教授 (90009605)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 複素多様体 / 保型形式 / 超幾何微分方程式 |
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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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