Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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TWO MEROMORPHIC FUNCTIONS SHARING FOUR PAIRS OF SMALL FUNCTIONS

  • Nguyen, Van An (Division of Mathematics Banking Academy) ;
  • Si, Duc Quang (Department of Mathematics Hanoi National University of Education)
  • Received : 2016.03.19
  • Accepted : 2017.03.10
  • Published : 2017.07.31
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Abstract

The purpose of this paper is twofold. The first is to show that two meromorphic functions f and g must be linked by a quasi-$M{\ddot{o}}bius$ transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-$M{\ddot{o}}bius$ transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by 4, where all zeros with multiplicities at least k > 865 are omitted. Moreover the explicit $M{\ddot{o}}bius$-transformation between such f and g is given. Our results are improvement of some recent results.

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References

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