Geometric study of special functions

我们构造了超几何函数和多元微分方程组的几个公式。(1)利用扭(余)同调群之间的交形式，给出了一些扭(余)同调群的Pfaffian的单调表示和联络矩阵。(2)对于具有与代数簇周期有关的特殊参数的超几何函数，我们给出了自同构型与超几何函数之间的一些恒等式。(3)用多元超几何函数表示由多项平均迭代所定义的一些极限。

We construct several formulas for hypergeometric functions and systems of differential equations of multi-variables. (1) By using the intersection forms defined between twisted (co)homology groups, we give monodromy representations and connection matrices of Pfaffians for some of them. (2) For hypergeometric functions with special parameters related to periods of algebraic varieties, we give some identities between automorphic forms and hypergeometric functions. (3) Some limits defined by the iteration of several means of several terms are expressed by hypergeometric functions of multi-variables.