Uniqueness theorems for entire functions whose difference polynomials share a meromorphic function of a smaller order

Volume 102 / 2011

Xiao-Min Li, Wen-Li Li, Hong-Xun Yi, Zhi-Tao Wen Annales Polonici Mathematici 102 (2011), 111-127 MSC: 30D35, 30D30. DOI: 10.4064/ap102-2-2

Abstract

We deal with uniqueness of entire functions whose difference polynomials share a nonzero polynomial CM, which corresponds to Theorem 2 of I. Laine and C. C. Yang [Proc. Japan Acad. Ser. A 83 (2007), 148–151] and Theorem 1.2 of K. Liu and L. Z. Yang [Arch. Math. 92 (2009), 270–278]. We also deal with uniqueness of entire functions whose difference polynomials share a meromorphic function of a smaller order, improving Theorem 5 of J. L. Zhang [J. Math. Anal. Appl. 367 (2010), 401–408], where the entire functions are of finite orders.

Authors

  • Xiao-Min LiDepartment of Mathematics
    Ocean University of China
    Qingdao, Shandong 266100
    People's Republic of China
    and
    Department of Physics and Mathematics
    University of Eastern Finland
    P.O. Box 111
    FI-80101 Joensuu, Finland
    e-mail
  • Wen-Li LiDepartment of Mathematics
    Ocean University of China
    Qingdao, Shandong 266100
    People's Republic of China
    e-mail
  • Hong-Xun YiDepartment of Mathematics
    Shandong University
    Jinan, Shandong 250100
    People's Republic of China
    e-mail
  • Zhi-Tao WenDepartment of Mathematics
    Ocean University of China
    Qingdao, Shandong 266100
    People's Republic of China
    and
    Department of Physics and Mathematics
    University of Eastern Finland
    P.O. Box 111
    FI-80101 Joensuu, Finland
    e-mail

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