On zeros of differences of meromorphic functions
Volume 100 / 2011
Annales Polonici Mathematici 100 (2011), 167-178
MSC: Primary 30D35; Secondary 39B12.
DOI: 10.4064/ap100-2-6
Abstract
Let $f$ be a transcendental meromorphic function and $g(z)=f(z+c_1)+\cdots+f(z+c_k)-kf(z)$ and $g_k(z)=f(z+c_1)\cdots f(z+c_k)-f^k(z)$. A number of results are obtained concerning the exponents of convergence of the zeros of $g(z)$, $g_k(z)$, ${g(z)}//{f(z)},$ and ${g_k(z)}//{f^k(z)}$.
