Distribution of zeros and shared values of
difference operators
Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 213-221
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
investigate distribution zeros shared values difference operator meromorphic functions particular transcendental meromorphic function finite order small number poles non zero complex constant delta geq small function respect delta equals infty infinitely many points uniqueness difference polynomials points fixed points proved
Affiliations des auteurs :
Jilong Zhang 1 ; Zongsheng Gao 2 ; Sheng Li 3
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author = {Jilong Zhang and Zongsheng Gao and Sheng Li},
title = {Distribution of zeros and shared values of
difference operators},
journal = {Annales Polonici Mathematici},
pages = {213--221},
publisher = {mathdoc},
volume = {102},
number = {3},
year = {2011},
doi = {10.4064/ap102-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap102-3-2/}
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Jilong Zhang; Zongsheng Gao; Sheng Li. Distribution of zeros and shared values of difference operators. Annales Polonici Mathematici, Tome 102 (2011) no. 3, pp. 213-221. doi: 10.4064/ap102-3-2
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