Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 2: 417 - 433

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

RESEARCH ARTICLE

Derivatives of meromorphic functions and exponential functions

  • Pai YANG , 1,2 ,
  • Liangwen LIAO 2 ,
  • Qiaoyu CHEN 3
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  • 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
  • 2. Department of Mathematics, Nanjing University, Nanjing 210093, China
  • 3. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China

Received date: 06 May 2015

Accepted date: 09 Feb 2018

Published date: 28 Mar 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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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 lim⁡¯r→∞T(r,f)r2=∞⁢     then      f'(z)=R(ez) has infinitely many solutions in the complex plane.

Key words： Meromorphic function; quasinormal family; Picard theorem

Cite this article

Pai YANG , Liangwen LIAO , Qiaoyu CHEN . Derivatives of meromorphic functions and exponential functions[J]. Frontiers of Mathematics in China, 2018 , 13(2) : 417 -433 . DOI: 10.1007/s11464-018-0691-2

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