On the singularities of the inverse to a meromorphic function of finite order.

Walter Bergweiler; Alexander Eremenko

Revista Matemática Iberoamericana (1995)

  • Volume: 11, Issue: 2, page 355-373
  • ISSN: 0213-2230

Abstract

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Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f.We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture of Hayman. The proof makes use of the iteration theory of meromorphic functions.

How to cite

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Bergweiler, Walter, and Eremenko, Alexander. "On the singularities of the inverse to a meromorphic function of finite order.." Revista Matemática Iberoamericana 11.2 (1995): 355-373. <http://eudml.org/doc/39474>.

@article{Bergweiler1995,
abstract = {Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f.We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture of Hayman. The proof makes use of the iteration theory of meromorphic functions.},
author = {Bergweiler, Walter, Eremenko, Alexander},
journal = {Revista Matemática Iberoamericana},
keywords = {Función meromorfa; Superficies Riemann; Ley límite; Teoría de singularidades},
language = {eng},
number = {2},
pages = {355-373},
title = {On the singularities of the inverse to a meromorphic function of finite order.},
url = {http://eudml.org/doc/39474},
volume = {11},
year = {1995},
}

TY - JOUR
AU - Bergweiler, Walter
AU - Eremenko, Alexander
TI - On the singularities of the inverse to a meromorphic function of finite order.
JO - Revista Matemática Iberoamericana
PY - 1995
VL - 11
IS - 2
SP - 355
EP - 373
AB - Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f.We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture of Hayman. The proof makes use of the iteration theory of meromorphic functions.
LA - eng
KW - Función meromorfa; Superficies Riemann; Ley límite; Teoría de singularidades
UR - http://eudml.org/doc/39474
ER -

Citations in EuDML Documents

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  1. Ha Huy Khoai, Vu Hoai An, Value distribution problem for p -adic meromorphic functions and their derivatives
  2. Zong-Xuan Chen, Kwang Ho Shon, Properties of differences of meromorphic functions
  3. Sujoy Majumder, Rajib Mandal, Generalizations on the results of Cao and Zhang
  4. Soniya Sultana, Pulak Sahoo, Uniqueness results for differential polynomials sharing a set
  5. Sujoy Majumder, On the generalization of two results of Cao and Zhang
  6. Sujoy Majumder, Rajib Mandal, Uniqueness of meromorphic functions concerning value sharing of nonlinear differential monomials
  7. Sujoy Majumder, Nonlinear differential monomials sharing two values

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