Distribution of zeros and shared values of difference operators

Jilong Zhang, Zongsheng Gao, and Sheng Li. "Distribution of zeros and shared values of difference operators." Annales Polonici Mathematici 102.3 (2011): 213-221. <http://eudml.org/doc/280904>.

@article{JilongZhang2011,
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 $Δ^k_cf ≠ 0$ for n ≥ 2, and a is a small function with respect to f, then $fⁿΔ^k_cf$ equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.},
author = {Jilong Zhang, Zongsheng Gao, Sheng Li},
journal = {Annales Polonici Mathematici},
keywords = {meromorphic function; difference; shared value},
language = {eng},
number = {3},
pages = {213-221},
title = {Distribution of zeros and shared values of difference operators},
url = {http://eudml.org/doc/280904},
volume = {102},
year = {2011},
}

TY - JOUR
AU - Jilong Zhang
AU - Zongsheng Gao
AU - Sheng Li
TI - Distribution of zeros and shared values of difference operators
JO - Annales Polonici Mathematici
PY - 2011
VL - 102
IS - 3
SP - 213
EP - 221
AB - 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 $Δ^k_cf ≠ 0$ for n ≥ 2, and a is a small function with respect to f, then $fⁿΔ^k_cf$ equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
LA - eng
KW - meromorphic function; difference; shared value
UR - http://eudml.org/doc/280904
ER -