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On Homogeneous Differential Polynomials of Meromorphic Functions

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Abstract

In this paper, we study one conjecture proposed by W. Bergweiler and show that any transcendental meromorphic functions f(z) have the form exp(αz+β) if f(z)f″(z)–a(f′ (z))2≠0, where \( a \ne 1,\;\frac{{n \pm 1}} {n},\;n \in N \). Moreover, an analogous normality criterion is obtained.

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou 515063, P. R. China

    Wei Chuan Lin

  2. Department of Mathematics, Fujian Teachers University, Fuzhou 350007, P. R. China

    Wei Chuan Lin

  3. Department of Mathematics, Shandong University, Jinan 250100, P. R. China

    Hong Xun Yi

Authors
  1. Wei Chuan Lin
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  2. Hong Xun Yi
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Correspondence to Wei Chuan Lin.

Additional information

Supported by National Natural Science Foundation and Science Technology Promotion Foundation of Fujian Province (2003)

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Lin, W.C., Yi, H.X. On Homogeneous Differential Polynomials of Meromorphic Functions. Acta Math Sinica 21, 261–266 (2005). https://doi.org/10.1007/s10114-004-0326-2

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  • DOI: https://doi.org/10.1007/s10114-004-0326-2

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