Zeros of meromorphic functions with poles close to the real axis
Let \[ f(z)=\sum_{k=1}^\infty\frac{a_k}{z-z_k},\quad \lim_{k\to\infty}z_k=\infty,\quad \sum_{z_k\not=0}\left| \frac{a_k}{z_k}\right| <\infty. \] If the \(z_k\) lie sufficiently close to the real axis and the \(a_k\) are close in an average sense to the positive real axis then \(f\) has infinitely many zeros.
scientific article; zbMATH DE number 5285856