Comptes Rendus
no. 6
Analyse complexe
Picard-Hayman behavior of derivatives of meromorphic functions
Yan Xu1  ; Shirong Chen1 ; Peiyan Niu2
1 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R.China
2 School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, P.R.China
Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 753-756.

Let f be a transcendental meromorphic function on ℂ, and P(z),Q(z) be two polynomials with degP(z)>degQ(z). In this paper, we prove that: if f(z)=0⇒f′(z)=a(a nonzero constant), except possibly finitely many, then f′(z)-P(z)/Q(z) has infinitely many zeros. Our result extends or improves some previous related results due to Bergweiler–Pang, Pang–Nevo–Zalcman, Wang–Fang, and the author, et. al.

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DOI : 10.5802/crmath.96
Classification : 30D35, 30D45

Yan Xu 1 ; Shirong Chen 1 ; Peiyan Niu 2

1 School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, P.R.China
2 School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, P.R.China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Yan Xu; Shirong Chen; Peiyan Niu. Picard-Hayman behavior of derivatives of meromorphic functions. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6, pp. 753-756. doi : 10.5802/crmath.96. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.96/

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