no. 6
Analyse complexe
Picard-Hayman behavior of derivatives of meromorphic functions
Xu, Yan1  ; Chen, Shirong1 ; Niu, Peiyan2
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, Tome 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.96
Classification : 30D35, 30D45
Xu, Yan 1 ; Chen, Shirong 1 ; Niu, Peiyan 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 
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Xu, Yan; Chen, Shirong; Niu, Peiyan. Picard-Hayman behavior of derivatives of meromorphic functions. Comptes Rendus. Mathématique, Tome 358 (2020) no. 6, pp. 753-756. doi : 10.5802/crmath.96. http://www.numdam.org/articles/10.5802/crmath.96/

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