Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PAIRED HAYMAN CONJECTURE AND UNIQUENESS OF COMPLEX DELAY-DIFFERENTIAL POLYNOMIALS

  • Gao, Yingchun (Department of Mathematics Nanchang University) ;
  • Liu, Kai (Department of Mathematics Nanchang University)
  • Received : 2021.02.28
  • Accepted : 2021.08.19
  • Published : 2022.01.31
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Abstract

In this paper, the paired Hayman conjecture of different types are considered, namely, the zeros distribution of f(z)nL(g) - a(z) and g(z)nL(f) - a(z), where L(h) takes the derivatives h(k)(z) or the shift h(z+c) or the difference h(z+c)-h(z) or the delay-differential h(k)(z+c), where k is a positive integer, c is a non-zero constant and a(z) is a nonzero small function with respect to f(z) and g(z). The related uniqueness problems of complex delay-differential polynomials are also considered.

Keywords

Acknowledgement

The authors would like to thank the reviewer for useful comments and providing the references [1] and [18].

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