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Non-existence of meromorphic solutions of a Fermat type functional equation

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Aequationes mathematicae Aims and scope Submit manuscript

An Erratum to this article was published on 01 December 2009

Summary.

In this paper, we will first establish a uniqueness theorem for meromorphic functions f 1, f 2, and f 3 that satisfy the functional equation f 1 + f 2 + f 3 = 1, and as applications, we give some results about the existence of meromorphic solutions of f n + g n + h n = 1 and two results related to a conjecture of R. Brück.

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Authors and Affiliations

  1. School of Mathematics & System Sciences, Shandong University, Jinan, Shandong, 250100, P. R. China

    Lian-Zhong Yang & Ji-Long Zhang

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  1. Lian-Zhong Yang
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  2. Ji-Long Zhang
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Corresponding author

Correspondence to Lian-Zhong Yang.

Additional information

This work was supported by the NNSF of China (No. 10671109).

Manuscript received: February 7, 2007 and, in final form, May 2, 2007.

An erratum to this article is available at http://dx.doi.org/10.1007/s00010-009-2973-y.

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Yang, LZ., Zhang, JL. Non-existence of meromorphic solutions of a Fermat type functional equation. Aequ. math. 76, 140–150 (2008). https://doi.org/10.1007/s00010-007-2913-7

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  • DOI: https://doi.org/10.1007/s00010-007-2913-7

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