Distribution of zeros and shared values of difference operators

Volume 102 / 2011

Jilong Zhang, Zongsheng Gao, Sheng Li 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.

Authors

  • Jilong ZhangLMIB and School of Mathematics & Systems Science
    Beihang University
    Beijing, 100191, P.R. China
    e-mail
  • Zongsheng GaoBeihang University
    LMIB and School of Mathematics & Systems Science
    Beijing, 100191, P.R. China
    e-mail
  • Sheng LiCollege of Science
    Guangdong Ocean University
    Zhanjiang, Guangdong, 524008, P.R. China
    e-mail

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