Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T08:27:48.714Z Has data issue: false hasContentIssue false
  • English
  • Français

A CLUNIE LEMMA FOR DIFFERENCE AND q-DIFFERENCE POLYNOMIALS

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  02 October 2009

ZHI-BO HUANG  and
ZONG-XUAN CHEN
ZHI-BO HUANG
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China (email: [email protected])
ZONG-XUAN CHEN*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China (email: [email protected])
*
✉For correspondence; e-mail: [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.

The main purpose of this paper is to prove difference and q-difference counterparts of the Clunie lemma from the Nevanlinna theory of differential polynomials, where the difference and q-difference polynomials can contain many terms of maximal total degree in f(z) and its ( q-)shifts.

Keywords

Clunie lemmadifference polynomialq-difference polynomial

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 23 - 32
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The project was supported by the National Natural Science Foundation of China (No. 10871076), and partly supported by the School of Mathematical Sciences Foundation of SCNU, PR China.

References

[1]Barnett, D. C., Halburd, R. G., Orhonen, R. J. K. and Morgan, W., ‘Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations’, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 457–474.CrossRefGoogle Scholar
[2]Chiang, Y. M. and Feng, S. J., ‘On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane’, Ramanujan J. 16 (2008), 105–129.CrossRefGoogle Scholar
[3]Clunie, J., ‘On integral and meromorphic functions’, J. London Math. Soc. 37 (1962), 17–27.CrossRefGoogle Scholar
[4]Halburd, R. G. and Korhonen, R. J., ‘Difference analogue of the lemma on the logarithmic derivative with applications to difference equations’, J. Math. Anal. Appl. 314 (2006), 477–487.CrossRefGoogle Scholar
[5]He, Y. and Xiao, X., Algebroid Functions and Ordinary Differential Equations (Science Press, Beijing, 1988).Google Scholar
[6]Laine, I., Nevanlinna Theory and Complex Differential Equations (Walter de Gruyter, Berlin, 1993).CrossRefGoogle Scholar
[7]Laine, I. and Yang, C. C., ‘Clunie theorems for difference and q-difference polynomials’, J. London Math. Soc. 76 (2007), 556–566.Google Scholar
[8]Yang, C. C. and Ye, Z., ‘Estimates of the proximate function of differential polynomials’, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), 50–55.Google Scholar