MONODROMIC DIFFERENTIAL-EQUATIONS AND RIEMANN THETA-FUNCTIONS

We consider monodromic differential equations, i.e., equations involvi ng both derivatives and analytic continuation. They can be considered as a generalization of Riemann's study of the hypergeometric functions . In previous work we have completely solved a particular case of thes e equations, the Hurwitz equation that generalizes the exponential fun ctions. Here we show how to construct explicitly non-trivial solutions using theta functions.