A FAMILY OF ANALYTIC FUNCTIONS WHOSE MEMBERS HAVE EQUAL NUMBER OF ZEROS
ALEXANDER ABIAN
Abstract
Sufficient conditions are given for $pf(z)+qg(z)$ to have (in a region) the same number of zeros for every nonnegative real number $p$ and $q$ not both zero, where $f(z)$ as well as $g(z)$ is an analytic function.