Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ZERO DISTRIBUTION OF SOME DELAY-DIFFERENTIAL POLYNOMIALS

  • Laine, Ilpo (Department of Physics and Mathematics University of Eastern Finland) ;
  • Latreuch, Zinelaabidine (Department of Mathematics Laboratory of Pure and Applied Mathematics University of Mostaganem)
  • Received : 2020.01.17
  • Accepted : 2020.08.21
  • Published : 2020.11.30
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Abstract

Let f be a meromorphic function of finite order ρ with few poles in the sense Sλ(r, f) := O(rλ+ε) + S(r, f), where λ < ρ and ε ∈ (0, ρ - λ), and let g(f) := Σkj=1bj(z)f(kj)(z + cj) be a linear delay-differential polynomial of f with small meromorphic coefficients bj in the sense Sλ(r, f). The zero distribution of fn(g(f))s - b0 is considered in this paper, where b0 is a small function in the sense Sλ(r, f).

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Acknowledgement

The authors would like to thank the referee for his/her valuable comments which helped to complete some defects in the original version.

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