Zeros of meromorphic functions of the form $\sum _n\frac{c_n}{(z-t_n{)}^2}$

Abstract

We study zeros distribution for meromorphic functions of the form $\sum _n\frac{c_n}{(z-t_n{)}^2}$, where $\sum _n\frac{|c_n|}{|t_n{|}^2}<\infty$. We prove an analog of the classical Keldysh theorem and discuss a relation between zero-free functions of this form and second order differential equtions with polynomial coefficients.