| Budget Amount *help |
¥18,070,000 (Direct Cost: ¥13,900,000、Indirect Cost: ¥4,170,000)
Fiscal Year 2017: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
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| Outline of Final Research Achievements |
Theory of linear ordinary differential equation with polynomial coefficients has a long history. In the study of rigid local system N. Katz introduced and formulated a transformation by fractional derivatives as a middle convolution. After his work there happens a novel development in the theory. Regarding the positions of singular points of the equations as new variables, we obtain KZ equations with several variables including Appell's hypergeometric equations. Applying this transformation to these equations, we analyze fundamental problems for these equations. For example, we construct these equations, give integral representations of their solutions, obtain the conditions of their irreducibility and moreover give a structure of the solutions of the original ordinary differential equations.
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