Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T09:43:53.977Z Has data issue: false hasContentIssue false
  • English
  • Français

ZEROS OF DIFFERENTIAL POLYNOMIALS IN REAL MEROMORPHIC FUNCTIONS

Published online by Cambridge University Press:  23 May 2005

Walter Bergweiler ,
Alex Eremenko  and
Jim K. Langley
Walter Bergweiler
Affiliation:
Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D-24098 Kiel, Germany ([email protected])
Alex Eremenko
Affiliation:
Purdue University, West Lafayette, IN 47907, USA ([email protected])
Jim K. Langley
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate whether differential polynomials in real transcendental meromorphic functions have non-real zeros. For example, we show that if $g$ is a real transcendental meromorphic function, $c\in\mathbb{R}\setminus\{0\}$ and $n\geq3$ is an integer, then $g'g^n-c$ has infinitely many non-real zeros. If $g$ has only finitely many poles, then this holds for $n\geq2$. Related results for rational functions $g$ are also considered.

Keywords

Primary 30D35meromorphic functiondifferential polynomialreal zeros
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 2 , June 2005 , pp. 279 - 293
Copyright
Copyright © Edinburgh Mathematical Society 2005