| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
Hypergeometric equations are linear differential equations solved by an important class of functions called hypergeometric functions, while in certain sense Painleve equations may be thought of as nonlinear analogues of hypergeometric equations. Because of their nonlinearity, the study of Painleve equations requires various methods from dynamical systems. We constructed the phase space of a Painleve equation and gave a geometric characterization of it as an orbifold Hamiltonian dynamical system. We also discussed periodic solutions to another Painleve equation. As for hypergeometric functions we focused our attention on spacial-value formulas, especially on gamma product formulas, and obtained necessary conditions of arithmetic flavor for the existence of such formulas.
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