Five-value rich lines‎, ‎Borel directions and uniqueness of meromorphic functions

Document Type: Research Paper

Author

School of Mathematical Sciences‎, ‎Guizhou Normal University‎, ‎550001‎, ‎Guiyang‎, ‎P.R‎. ‎China ‎School of Computer Sciences and School of Sciences‎, ‎Beijing University of Posts and Telecommunications‎, ‎Beijing‎, ‎100876‎, ‎P.R‎. ‎China‎.

Abstract

For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ is its five-value rich line, and the inverse statement holds when $f$ is of infinite order.

Keywords

Main Subjects


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Volume 43, Issue 5
September and October 2017
Pages 1467-1478
  • Receive Date: 31 October 2015
  • Revise Date: 17 September 2016
  • Accept Date: 17 September 2016