Origine géométrique et représentation géométrique des fonctions elliptiques, abéliennes et de transcendantes d'ordres supérieurs.
We show that for a generic polynomial and an arbitrary differential 1-form with polynomial coefficients of degree , the number of ovals of the foliation , which yield the zero value of the complete Abelian integral , grows at most as as , where depends only on . The main result of the paper is derived from the following more general theorem on bounds for isolated zeros occurring in polynomial envelopes of linear differential equations. Let , , be a fundamental system of real solutions...