On the zeros of certain homogeneous differential polynomials

DOI10.1007/BF01188569zbMath0818.30021OpenAlexW1997027373MaRDI QIDQ1805499

Walter Bergweiler

Publication date: 18 May 1995

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01188569

zbMATH Keywords

iterationdynamicsfixed pointcritical valuemeromorphic functionasymptotic valueexceptional valuedifferential polynomial

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Dynamical systems over complex numbers (37F99)

Related Items (21)

Deficient values of derivatives of meromorphic functions in the class \(S\) ⋮ Critical values of slowly growing meromorphic functions ⋮ Entire solutions of binomial differential equations ⋮ Normal families and shared values of holomorphic functions ⋮ A theorem on homogeneous differential polynomials ⋮ Non-real zeroes of real entire derivatives ⋮ On normal families of meromorphic functions ⋮ Entire solutions of certain type binomial differential equations ⋮ Non-linear homogeneous differential polynomials ⋮ On a conjecture of W. Bergweiler ⋮ Normal families of meromorphic functions with multiple zeros and poles ⋮ On the number of non-real zeroes of a homogeneous differential polynomial and a generalisation of the Laguerre inequalities ⋮ A lower bound for the number of zeros of a meromorphic function and its second derivative ⋮ Meromorphic functions in the class \(S\) and the zeros of the second derivative ⋮ Extending two fixpoint theorems of Langley and Zheng ⋮ Non-real zeros of derivatives of real meromorphic functions of infinite order ⋮ On differential polynomials, fixpoints and critical values of meromorphic functions ⋮ Normal families and shared values of meromorphic functions. II. ⋮ On homogeneous differential polynomials of meromorphic functions ⋮ Normality and exceptional values of derivatives ⋮ Normality of meromorphic functions with multiple zeros and shared values

Cites Work

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• Picard values of meromorphic functions and their derivatives
• Dynamical properties of some classes of entire functions
• Über die Nullstellen homogener Differentialpolynome
• On the singularities of the inverse to a meromorphic function of finite order
• Über eine Vermutung von Hayman
• Iteration of meromorphic functions
• Proof of a Conjecture of Hayman Concerning f and f ″
• An Extension of Schwarz's Lemma

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