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Picard type theorems concerning certain small functions

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Abstract

Let f(z) be a meromorphic function in the complex plane, whose zeros have multiplicity at least k + 1 (k ≥ 2). If sin z is a small function with respect to f(z), then f(k)(z) − P(z) sinz has infinitely many zeros in the complex plane, where P(z) is a nonzero polynomial of deg(P(z)) ≠ 1.

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Authors and Affiliations

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

    Pai Yang

  2. School of of Mathematics and Information Science, He’nan University of Economics and Law, Zhengzhou, 450046, P. R. China

    Lei Qiao

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  1. Pai Yang
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  2. Lei Qiao
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Correspondence to Pai Yang.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11301140, 11671191 and 11501367), China Postdoctoral Science Foundation (Grant No. 2015M571726) and the Project of Sichuan Provincial Department of Education (Grant No. 15ZB0172)

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Yang, P., Qiao, L. Picard type theorems concerning certain small functions. Acta. Math. Sin.-English Ser. 33, 1275–1286 (2017). https://doi.org/10.1007/s10114-017-6137-z

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  • DOI: https://doi.org/10.1007/s10114-017-6137-z

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