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Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 417–433 | Cite as

Derivatives of meromorphic functions and exponential functions

  • Pai Yang
  • Liangwen Liao
  • Qiaoyu Chen
Research Article
  • 30 Downloads

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(e z ) has infinitely many solutions in the complex plane.

Keywords

Meromorphic function quasinormal family Picard theorem 

MSC

30D35 30D45 

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Notes

Acknowledgements

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

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Applied MathematicsChengdu University of Information TechnologyChengduChina
  2. 2.Department of MathematicsNanjing UniversityNanjingChina
  3. 3.School of Statistics and MathematicsShanghai Lixin University of Accounting and FinanceShanghaiChina

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