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Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences

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Abstract

Let f(z) be a transcendental meromorphic function in the complex plane of hyper-order strictly less than 1. It is shown that if f(z) and its nth exact difference Δnf(z) (≢ 0) share three distinct periodic functions \({\rm{a, b, c}} \in \mathcal{\hat{S}}(f)\) with period 1 CM, where \(\mathcal{\hat{S}}(f) = \mathcal{S}(f)\cup\{{\infty}\}\) and \(\mathcal{S}(f)\) denotes the set of all small functions of f(z), then Δnf(z) ≡ f(z).

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Beihang University, LMIB, Beijing, 100191, P. R. China

    Z. Gao & J. Zhang

  2. Department of Physics and Mathematics, University of Eastern Finland, P.O.Box 111, FI-80801, Joensuu, Finland

    R. Korhonen & Y. Zhang

Authors
  1. Z. Gao
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  2. R. Korhonen
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  3. J. Zhang
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  4. Y. Zhang
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Corresponding author

Correspondence to R. Korhonen.

Additional information

The first, third and fourth authors were supported in part by the NNSF of China no. 11171013, 11371225, 11201014 and the Fundamental Research Funds for the Central University.

The second author was supported by the Academy of Finland grants #286877, #268009.

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Gao, Z., Korhonen, R., Zhang, J. et al. Uniqueness of Meromorphic Functions Sharing Values with their nth Order Exact Differences. Anal Math 45, 321–334 (2019). https://doi.org/10.1007/s10476-018-0605-2

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  • DOI: https://doi.org/10.1007/s10476-018-0605-2

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