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On the value distribution of ƒ + a(ƒ′)n

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Abstract

Let ƒ be a transcendental meromorphic function, a a nonzero finite complex number, and n ⩾ 2 a positive integer. Then ƒ + a(ƒ′)n assumes every complex value infinitely often. This answers a question of Ye for n = 2. A related normality criterion is also given.

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Authors and Affiliations

  1. Institute of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China

    MingLiang Fang

  2. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Lawrence Zalcman

Authors
  1. MingLiang Fang
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  2. Lawrence Zalcman
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Corresponding author

Correspondence to MingLiang Fang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10771076), the Natural Science Foundation of Guangdong Province, China (Grant No. 07006700) and by the German-Israeli Foundation for Scientific Research and Development (Grant No. G-809-234.6/2003)

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Fang, M., Zalcman, L. On the value distribution of ƒ + a(ƒ′)n . Sci. China Ser. A-Math. 51, 1196–1202 (2008). https://doi.org/10.1007/s11425-008-0022-2

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  • DOI: https://doi.org/10.1007/s11425-008-0022-2

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