STUDIES ON D-MODULES DERIVED FROM CONFLUENT HYPERGEOMETRIC DIFFERENTIAL EQUATIONS

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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.