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A Positive Answer for 3IM+1CM Problem with a General Difference Polynomial

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  • Huicai Xu
  • Shugui Kang
  • Qingcai Zhang
  • Li Li

Abstract

In this paper, the 3IM+1CM theorem with a general difference polynomial Lz,f will be established by using new methods and technologies. Note that the obtained result is valid when the sum of the coefficient of Lz,f is equal to zero or not. Thus, the theorem with the condition that the sum of the coefficient of Lz,f is equal to zero is also a good extension for recent results. However, it is new for the case that the sum of the coefficient of Lz,f is not equal to zero. In fact, the main difficulty of proof is also from this case, which causes the traditional theorem invalid. On the other hand, it is more interesting that the nonconstant finite-order meromorphic function f can be exactly expressed for the case f≡−Lz,f. Furthermore, the sharpness of our conditions and the existence of the main result are illustrated by examples. In particular, the main result is also valid for the discrete analytic functions.

Suggested Citation

  • Huicai Xu & Shugui Kang & Qingcai Zhang & Li Li, 2021. "A Positive Answer for 3IM+1CM Problem with a General Difference Polynomial," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-9, November.
    • Handle: RePEc:hin:jnddns:7113065
    DOI: 10.1155/2021/7113065
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