Factorization of Complex Analytic Functions Algebraically Dependent on Space Curves and Applications to Compatible Functional and Differential Equations

In this article, we characterize a system {f, g, h} of meromorphic functions in C-3 that are algebraically dependent. We consider the algebraic dependence described by space curves of genus zero or genus one, and we show that all three functions share a right common factor. We define functional and differential equations associated to space curves and study the existence and the forms of their complex analytic solutions.

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In this article, a system {f, g, h} of meromorphic functions in C-3 that are algebraically dependent is characterized. The algebraic dependence described by space curves of genus zero or genus one is considered, and it is shown that all three functions share a right common factor. Functional and differential equations associated to space curves are defined and the existence and the forms of their complex analytic solutions are studied.