STUDIES ON D-MODULES DERIVED FROM CONFLUENT HYPERGEOMETRIC DIFFERENTIAL EQUATIONS

1.利用与Koszul复形类似的D-模的投影分解，计算由合流超几何微分方程定义的D-模的解复形的上同调群，这些方程的值在形式幂级数环和Gevrey阶形式幂级数环的芽层中，这是根据Takayama 2所做的“KAN”（计算代数分析的一个系统）中的建议信息而发明的。利用具有特定参数的合流超几何函数与广义Airy函数之间的关系，得到广义Airy函数约束的渐近展开式3.利用多元渐近分析中的消失定理给出发散解系数的近似公式4.应用这一理论，构造了同调群和上同调群在复射影线上的交理论，这些群是由正则奇异或非正则奇异的联络和合流超几何函数满足的二次关系定义的，作为周期关系的一种模拟。

1. Calculation of cohomology groups of solution complex of D-modules defined by confluent hypergeometric differential equations with values in the sheaves of germs of formal power-series ring and formal power-series ring with Gevrey order, by using projective resolutions of the D-modules similar to Koszul complex, which was invented by suggested information from 'KAN(a system' of computational algebraic analysis) made by Takayama2. Asymptotic expansions of restrictions of generalized Airy functions by using relations between confluent hypergeometric functions with particular parameters and generalized Airy functions3. Approximation formulas of coefficients of divergent solutions by using a vanishing theorem in asymptotic analysis in several variables4. Constructionf of theory of intersection on the complex projective line for homology and cohomology groups defined by connections which are regular singular or not, and quadratic relations satisfied by confluent hypergeometric functions, as an analogue of period relations, by applying this theory.