Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T02:06:24.024Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON VALUE DISTRIBUTION OF DIFFERENCE POLYNOMIALS

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  05 March 2010

K. LIU  and
I. LAINE
K. LIU*
Affiliation:
Department of Mathematics, Nanchang University, Nanchang, Jiangxi, 330031, PR China
I. LAINE
Affiliation:
Department of Mathematics, University of Joensuu, PO Box 111, FI-80101 Joensuu, Finland (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.

In this paper, we investigate the value distribution of difference polynomials and prove some difference analogues of results of Hayman and the Brück conjecture.

Keywords

shiftdifference operatorfinite order

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 353 - 360
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The second author has been partially supported by the Academy of Finland grant 124954.

References

[1]Brück, R., ‘On entire functions which share one value CM with their first derivative’, Results in Math. 30 (1996), 21–24.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’, The Ramanujan J. 16 (2008), 105–129.Google Scholar
[3]Clunie, J., ‘On integral and meromorphic functions’, J. Lond. 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.Google Scholar
[5]Hayman, W. K., ‘Picard values of meromorphic functions and their derivatives’, Ann. of Math. (2) 70 (1959), 9–42.Google Scholar
[6]Hayman, W. K., Meromorphic Functions (Clarendon Press, Oxford, 1964).Google Scholar
[7]Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J. and Zhang, J. L., ‘Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity’, J. Math. Anal. Appl. 355 (2009), 352–363.Google Scholar
[8]Laine, I., Nevanlinna Theory and Complex Differential Equations (Walter de Gruyter, Berlin, 1993).Google Scholar
[9]Yang, C.-C. and Yi, H.-X., Uniqueness Theory of Meromorphic Functions (Kluwer, Dordrecht, 2003).Google Scholar