JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 78-83.doi: 10.6040/j.issn.1671-9352.0.2024.107

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Value distribution of rational function with multiple zero

YANG Pai1, LIN Huli1, YANG Jinhua2   

  1. 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China;
    2. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830017, Xinjiang, China
  • Published:2026-04-08

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Abstract: Let n≥1 be an integer, and f(z) be a meromorphic function in complex plane, whose zeros are multiple. If f '(z)≠zn for each z∈C, then f(z) must be restricted to specific forms of rational function.

Key words: rational function, meromorphic function, value distribution, multiple zeros

CLC Number: 

  • O174.5
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