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.