OVERCONVERGENCE AND ZEROS OF SEQUENCES OF RATIONAL FUNCTIONS

In the present paper we consider sequences of rational functions with a bounded number or free poles con-verging uniformly with a maximum geometric rate to a holomorphic function on a regular set,and we examinethe limiting distribution of the Zeros and its relations with the phenomenon of overconvergence.Our resultsfurther extend the well known classical theory of overconvergence and the zeros of sections of Taylor series.