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Non-Linear Homogeneous Differential Polynomials

Non-Linear Homogeneous Differential Polynomials We apply lemmas of Mues and Steinmetz from [4] to non-linear homogeneous differential polynomials in the meromorphic function f and f (k) with coefficients which are O(log r) + O(T(r, f)) in order to find sufficient conditions for f to be of the form Re P where R is a rational function and P is a polynomial. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Non-Linear Homogeneous Differential Polynomials

Buck, Matthew
Computational Methods and Function Theory , Volume 12 (1) – Nov 30, 2011
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6 pages

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321818
Publisher site
See Article on Publisher Site

Abstract

We apply lemmas of Mues and Steinmetz from [4] to non-linear homogeneous differential polynomials in the meromorphic function f and f (k) with coefficients which are O(log r) + O(T(r, f)) in order to find sufficient conditions for f to be of the form Re P where R is a rational function and P is a polynomial.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Nov 30, 2011

References

  • On the zeros of certain homogeneous differential polynomials
    Bergweiler, W
  • On integral and meromorphic functions
    Clunie, J
  • Meromorphic Functions
    Hayman, W K
  • The theorem of Tumura-Clunie for meromorphic functions
    Mues, E; Steinmetz, N
  • On the zeros of a homogeneous differential polynomial of a meromorphic function
    Tohge, K