Distribution of zeros and shared values of difference operators
Volume 102 / 2011
Annales Polonici Mathematici 102 (2011), 213-221
MSC: 39A05, 30D35.
DOI: 10.4064/ap102-3-2
Abstract
We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if $f$ is a transcendental meromorphic function of finite order with a small number of poles, $c$ is a non-zero complex constant such that $\Delta ^k_cf\not =0$ for $n\geq 2$, and $a$ is a small function with respect to $f$, then $f^n\Delta ^k_cf$ equals $a$ $(\not =0, \infty )$ at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
