Another improvement of Montel's criterion

Kodai Mathematical Journal

Yan Xu¹ 

[1] Institute of Mathematics School of Mathematics Nanjing Normal University

关键词: Meromorphic function;    Riemann-Hurwitz formula;    normal family;    Montel's criterion;   

DOI  :  10.2996/kmj/1364562719

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(10)Let ${\cal F}$ be a family of meromorphic functions defined in a domain D ⊂ C, let ψ1, ψ2 and ψ3 be three meromorphic functions such that ψi(z) $\not\equiv$ ψj(z) (i ≠ j) in D, one of which may be ∞ identically, and let l1, l2 and l3 be positive integers or ∞ with 1/l1 + 1/l2 + 1/l3 < 1. Suppose that, for each f ∈ ${\cal F}$ and z ∈ D, (1) all zeros of f – ψi have multiplicity at least li for i = 1,2,3; (2) f(z0) ≠ ψi(z0) if there exist i, j ∈ {1,2,3} (i ≠ j) and z0 ∈ D such that ψi(z0) = ψj(z0). Then ${\cal F}$ is normal in D. This improves and generalizes Montel's criterion.

【 授权许可】

Unknown