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Derivatives of meromorphic functions with multiple zeros and elliptic functions

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Abstract

Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple except finitely many and T(r, h) = o{T(r, f)} as r→∞, then f′ = h has infinitely many solutions (including poles).

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, 200062, P. R. China

    Pai Yang

  2. College of Mathematics, Chengdu University of Information Technology, Chengdu, 610225, P. R. China

    Pai Yang

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

    Shahar Nevo

Authors
  1. Pai Yang
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  2. Shahar Nevo
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Correspondence to Pai Yang.

Additional information

The second author is supported by the Israel Science Foundation (Grant No. 395/2007)

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Yang, P., Nevo, S. Derivatives of meromorphic functions with multiple zeros and elliptic functions. Acta. Math. Sin.-English Ser. 29, 1257–1278 (2013). https://doi.org/10.1007/s10114-013-2375-x

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  • DOI: https://doi.org/10.1007/s10114-013-2375-x

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