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Derivatives of meromorphic functions and exponential functions

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Abstract

We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a Möbius transformation. If \({\overline {\lim } _{r \to \infty }}\frac{{T\left( {r,f} \right)}}{{{r^2}}} = \infty \) then fz) = R(ez) has infinitely many solutions in the complex plane.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11501367, 11671191)

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Correspondence to Pai Yang.

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Yang, P., Liao, L. & Chen, Q. Derivatives of meromorphic functions and exponential functions. Front. Math. China 13, 417–433 (2018). https://doi.org/10.1007/s11464-018-0691-2

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  • DOI: https://doi.org/10.1007/s11464-018-0691-2

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