On small circles containing zeros and ones of analytic functions

Abstract

Gol'dberg considered the class of functions with unequal positive numbers of zeros and ones inside the unit disc. The maximum modulus of zeros and ones in this class is bounded from below by a universal constant. This constant determines the limits of certain controller designs as well as covering regions of certain composites with schlicht functions. Considering lower bounds in a zero-free region of the extremal function the best known estimates of this constant are improved.