Arithmetic relations between modular forms and hypergeometric functions in several variables
Project/Area Number |
20540007
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Chiba University |
Principal Investigator |
SIGA Hironori Chiba University, 理工学術院, 教授 (90009605)
|
Project Period (FY) |
2008 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
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)
|
Keywords | 複素多様体 / 保型形式 / 超幾何微分方程式 / Hypergeometric Function / Picard modular form / Shimura variety / Abelin variety / Arithmetic Geometric Mean / Theta Function / Modular Form / Picard modular function / Arithmetic-Geometric Mean / Modular form / Schwarz Map |
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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Report
(4 results)
Research Products
(24 results)